CUET Mathematics - Algebra - Probability | Free Questions - Page 12

Q1:

2022: 17 Aug Shift 2

Algebra

>

Probability

Medium

Core

Bag A contains 2 red and 3 white balls, Bag B contains 3 red and 2 white balls. If a ball is drawn at random and is found to be red, then the probability that it was drawn from bag B, is :

$\frac{3}{5}$

$\frac{2}{5}$

$\frac{4}{5}$

$\frac{1}{5}$

Correct Answer

Option 1

Correct Answer

Explanation

Q2:

2022: 17 Aug Shift 2

Algebra

>

Probability

Hard

Core

Three friends A, B and C are playing with a pair of dice. They throw two dice alternately. Coming of a doublet on two dice leads to a success and the game stops. If A starts the game, then the probability of his winning, is :

$\frac{1}{216}$

$\frac{36}{91}$

$\frac{7}{216}$

$\frac{125}{216}$

Correct Answer

Option 2

Correct Answer

Explanation

Q3:

2022: 17 Aug Shift 2

Algebra

>

Probability

Medium

Core

If $A$ and $B$ are independent events such that $0 < P(A) < 1$ and $0 < P(B) < 1$ , then identify the correct statements.

(A) $A$ and $B'$ are independent

(B) $A'$ and $B$ are independent

(C) $A$ and $B$ are mutually exclusive

(D) $A'$ and $B'$ are independent

Choose the correct answer from the options given below :

A, B and C only

B and C only

B, C and D only

A, B and D only

Correct Answer

Option 4

Correct Answer

Explanation

Q4:

2022: 17 Aug Shift 2

Algebra

>

Probability

Hard

Core

A letter is expected to come either from city 'SURAT' or from city 'RAMPUR' through post office. If on the way, envelope containing the letter is damaged and only two consecutive alphabets RA are visible on it, then the probability that letter comes from the city 'SURAT' is :

$\frac{5}{9}$

$\frac{4}{9}$

$\frac{5}{8}$

$\frac{3}{8}$

Correct Answer

Option 1

Correct Answer

Explanation

Q5:

2022: 17 Aug Shift 2

Algebra

>

Probability

Easy

Core

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

Based on the above informations, answer the question :

The probability of the person tested as COVID positive, given that he is actually having COVID is :

$\frac{1}{1000}$

$\frac{1}{10}$

$\frac{8}{10}$

$\frac{9}{10}$

Correct Answer

Option 4

Correct Answer

Explanation

Q6:

2022: 17 Aug Shift 2

Algebra

>

Probability

Easy

Core

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

Based on the above informations, answer the question :

The probability of the person to be tested as COVID positive, given that he is actually not having COVID is :

$\frac{1}{100}$

$\frac{9}{10}$

$\frac{1}{10}$

$\frac{99}{100}$

Correct Answer

Option 1

Correct Answer

Explanation

Q7:

2022: 17 Aug Shift 2

Algebra

>

Probability

Easy

Core

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

Based on the above informations, answer the question :

The probability that randomly selected person from a population, not having COVID is :

0.998

0.999

0.001

0.990

Correct Answer

Option 2

Correct Answer

Explanation

Q8:

2022: 17 Aug Shift 2

Algebra

>

Probability

Medium

Core

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

Based on the above informations, answer the question :

The probability that the selected person will be diagonosed as COVID positive is :

$\frac{1008}{10000}$

$\frac{803}{100000}$

$\frac{1089}{10000}$

$\frac{1089}{100000}$

Correct Answer

Option 4

Correct Answer

Explanation

Q9:

2022: 17 Aug Shift 2

Algebra

>

Probability

Medium

Core

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

Based on the above informations, answer the question :

The probability that the person is actually having COVID given that he is tested as COVID positive is :

$\frac{10}{121}$

$\frac{90}{1099}$

$\frac{1}{121}$

$\frac{89}{1089}$

Correct Answer

Option 1

Correct Answer

Explanation

Q10:

2022: 6 Aug Shift 2

Algebra

>

Probability

Medium

Core

If the mean and variance of a binomially distributed random variable X are 4 and 2 respectively, then $P(X = 2)$ is equal to

$\frac{7}{32}$

$\frac{1}{32}$

$\frac{7}{64}$

$\frac{1}{8}$

Correct Answer

Option 3

Correct Answer

Explanation

Q11:

2022: 6 Aug Shift 2

Algebra

>

Probability

Easy

Core

Which is the most suitable definition for random variable among the options given below:

It is a relation between the events of a sample space and the numbers in [0,1].

It is a function defined from the sample space of a random experiment to the set of real numbers.

It is a table containing probability values

It is a function from the set of natural numbers to the numbers in [0,1]

Correct Answer

Option 2

Correct Answer

Explanation

Q12:

2022: 6 Aug Shift 2

Algebra

>

Probability

Medium

Core

There are three identical boxes I, II and III, each containing two balls. In box I, both balls are red, In box II, both balls are blue and box III contains one blue ball and one red ball. A boy randomly chooses a box and takes out a ball at random from it. If the ball is red, then the probability that the other ball in the box is also red colour is:

$\frac{1}{2}$

$\frac{2}{3}$

$0$

$1$

Correct Answer

Option 2

Correct Answer

Explanation

Q13:

2022: 6 Aug Shift 2

Algebra

>

Probability

Easy

Core

If A and B are two independent events such that $P(A) = 0.4$ , and $P(B) = 0.5$ , then P (neither A nor B) is

$0.24$

$0.30$

$0.25$

$0.28$

Correct Answer

Option 2

Correct Answer

Explanation

Q14:

2022: 6 Aug Shift 2

Algebra

>

Probability

Easy

Core

A student was doing a project work, involving a school survey, to find the number of hours spent on study by students, on a randomly selected school day. At the end of the survey he prepared the following report related to the data.

Let x denote the number of hours spent on study by students on a randomly selected school day

then,

$P(X = x) = \begin{cases} 0.2, & \text{if } x = 0 \\ kx, & \text{if } x = 1 \text{ or } x = 2 \\ k(6-x), & \text{if } x = 3 \text{ or } x = 4 \\ 0, & \text{otherwise} \end{cases}$

where k is unknown constant

Based on the above information answer the Questions

The value of $k$ is

$0.1$

$0.2$

$0.25$

$0.125$

Correct Answer

Option 1

Correct Answer

Explanation

Q15:

2022: 6 Aug Shift 2

Algebra

>

Probability

Easy

Core

A student was doing a project work, involving a school survey, to find the number of hours spent on study by students, on a randomly selected school day. At the end of the survey he prepared the following report related to the data.

Let x denote the number of hours spent on study by students on a randomly selected school day

then,

$P(X = x) = \begin{cases} 0.2, & \text{if } x = 0 \\ kx, & \text{if } x = 1 \text{ or } x = 2 \\ k(6-x), & \text{if } x = 3 \text{ or } x = 4 \\ 0, & \text{otherwise} \end{cases}$

where k is unknown constant

Based on the above information answer the Questions

The probability that the study time of students is not more than one hour.

$0.4$

$0.3$

$0.2$

$0.1$

Correct Answer

Option 2

Correct Answer

Explanation

Q16:

2022: 6 Aug Shift 2

Algebra

>

Probability

Easy

Core

A student was doing a project work, involving a school survey, to find the number of hours spent on study by students, on a randomly selected school day. At the end of the survey he prepared the following report related to the data.

Let x denote the number of hours spent on study by students on a randomly selected school day

then,

$P(X = x) = \begin{cases} 0.2, & \text{if } x = 0 \\ kx, & \text{if } x = 1 \text{ or } x = 2 \\ k(6-x), & \text{if } x = 3 \text{ or } x = 4 \\ 0, & \text{otherwise} \end{cases}$

where k is unknown constant

Based on the above information answer the Questions

The probability that the study time of students is at least 3 hours

$0.5$

$0.2$

$0.8$

$0.7$

Correct Answer

Option 1

Correct Answer

Explanation

Q17:

2022: 6 Aug Shift 2

Algebra

>

Probability

Easy

Core

A student was doing a project work, involving a school survey, to find the number of hours spent on study by students, on a randomly selected school day. At the end of the survey he prepared the following report related to the data.

Let x denote the number of hours spent on study by students on a randomly selected school day

then,

$P(X = x) = \begin{cases} 0.2, & \text{if } x = 0 \\ kx, & \text{if } x = 1 \text{ or } x = 2 \\ k(6-x), & \text{if } x = 3 \text{ or } x = 4 \\ 0, & \text{otherwise} \end{cases}$

where k is unknown constant

Based on the above information answer the Questions

The probability that the study time of students is exactly 2 hours

$0.4$

$0.5$

$0.7$

$0.2$

Correct Answer

Option 4

Correct Answer

Explanation

Q18:

2022: 6 Aug Shift 2

Algebra

>

Probability

Easy

Core

A student was doing a project work, involving a school survey, to find the number of hours spent on study by students, on a randomly selected school day. At the end of the survey he prepared the following report related to the data.

Let x denote the number of hours spent on study by students on a randomly selected school day

then,

$P(X = x) = \begin{cases} 0.2, & \text{if } x = 0 \\ kx, & \text{if } x = 1 \text{ or } x = 2 \\ k(6-x), & \text{if } x = 3 \text{ or } x = 4 \\ 0, & \text{otherwise} \end{cases}$

where k is unknown constant

Based on the above information answer the Questions

The probability that the study time of students is at least 1 hour

$0.2$

$0.7$

$0.8$

$0.6$

Correct Answer

Option 3

Correct Answer

Explanation

Q19:

2022: 4 Aug Shift 1

Algebra

>

Probability

Easy

Core

The probability distribution of a discrete random variable X is given as :

x	0	1	2	3	4
P(X=x)	0.1	k	2k	2k	k

The value of K is:

0.16

0.18

0.15

0.25

Correct Answer

Option 3

Correct Answer

Explanation

Q20:

2022: 4 Aug Shift 1

Algebra

>

Probability

Easy

Core

Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. The probability distribution of the number of kings will be:

x	0	1	2
P(X=x)	$\frac{1}{169}$	$\frac{24}{169}$	$\frac{144}{169}$

x	0	1	2
P(X=x)	$\frac{24}{169}$	$\frac{144}{169}$	$\frac{1}{169}$

x	0	1	2
P(X=x)	$\frac{1}{169}$	$\frac{24}{169}$	$\frac{144}{169}$

x	0	1	2
P(X=x)	$\frac{144}{169}$	$\frac{24}{169}$	$\frac{1}{169}$

Correct Answer

Option 4

Correct Answer

Explanation

Q21:

2022: 4 Aug Shift 1

Algebra

>

Probability

Easy

Core

If A and B are two independent events with $P(A) = \frac{1}{5}$ and $P(B) = \frac{1}{3}$ , then $P(A'/B)$ is:

$\frac{4}{5}$

$\frac{1}{15}$

$\frac{8}{15}$

$\frac{2}{3}$

Correct Answer

Option 1

Correct Answer

Explanation

Q22:

2022: 4 Aug Shift 1

Algebra

>

Probability

Easy

Core

If two numbers are selected at random from the first 25 natural numbers, then the probability that their sum will be odd is:

$\frac{13}{50}$

$\frac{156}{625}$

$\frac{312}{625}$

$\frac{13}{25}$

Correct Answer

Option 4

Correct Answer

Explanation

Q23:

2022: 4 Aug Shift 1

Algebra

>

Probability

Easy

Core

A doctor is to visit a patient. From the past experiences, it is known that the probabilities of his coming by cab, metro, bike or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4 respectively. The probabilities that he will be late are 0.25, 0.3, 0.35 and 0.1 if he comes by cab, metro, bike and by other means of transport respectively. using this information about the doctor, answer the following questions :

When the doctor arrives late, what is the probability that he comes by metro?

$\frac{5}{4}$

$\frac{2}{7}$

$\frac{5}{21}$

$\frac{1}{6}$

Correct Answer

Option 2

Correct Answer

Explanation

Q24:

2022: 4 Aug Shift 1

Algebra

>

Probability

Easy

Core

A doctor is to visit a patient. From the past experiences, it is known that the probabilities of his coming by cab, metro, bike or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4 respectively. The probabilities that he will be late are 0.25, 0.3, 0.35 and 0.1 if he comes by cab, metro, bike and by other means of transport respectively. using this information about the doctor, answer the following questions :

When the doctor arrives late, what is the probability that he comes by cab?

$\frac{4}{21}$

$\frac{1}{7}$

$\frac{5}{14}$

$\frac{2}{21}$

Correct Answer

Option 3

Correct Answer

Explanation

Q25:

2022: 4 Aug Shift 1

Algebra

>

Probability

Easy

Core

A doctor is to visit a patient. From the past experiences, it is known that the probabilities of his coming by cab, metro, bike or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4 respectively. The probabilities that he will be late are 0.25, 0.3, 0.35 and 0.1 if he comes by cab, metro, bike and by other means of transport respectively. using this information about the doctor, answer the following questions :

When the doctor arrives late, what is the probability that he comes by bike?

$\frac{5}{21}$

$\frac{4}{7}$

$\frac{5}{6}$

$\frac{1}{6}$

Correct Answer

Option 4

Correct Answer

Explanation

Q26:

2022: 4 Aug Shift 1

Algebra

>

Probability

Easy

Core

A doctor is to visit a patient. From the past experiences, it is known that the probabilities of his coming by cab, metro, bike or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4 respectively. The probabilities that he will be late are 0.25, 0.3, 0.35 and 0.1 if he comes by cab, metro, bike and by other means of transport respectively. using this information about the doctor, answer the following questions :

When the doctor arrives late, what is the probability that he comes by other means of transport?

$\frac{5}{6}$

$\frac{5}{14}$

$\frac{4}{21}$

$\frac{2}{7}$

Correct Answer

Option 3

Correct Answer

Explanation

Q27:

2022: 4 Aug Shift 1

Algebra

>

Probability

Easy

Core

A doctor is to visit a patient. From the past experiences, it is known that the probabilities of his coming by cab, metro, bike or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4 respectively. The probabilities that he will be late are 0.25, 0.3, 0.35 and 0.1 if he comes by cab, metro, bike and by other means of transport respectively. using this information about the doctor, answer the following questions :

What is the probability that the doctor arrives late ?

0.17

0.21

1

0.5

Correct Answer

Option 2

Correct Answer

Explanation

Q28:

2022: 10 Aug Shift 1

Algebra

>

Probability

Easy

Core

A die is tossed four times. The probability of getting an odd number at least once, is

$\frac{1}{16}$

$\frac{10}{16}$

$\frac{4}{16}$

$\frac{15}{16}$

Correct Answer

Option 4

Correct Answer

Explanation

Q29:

2022: 10 Aug Shift 1

Algebra

>

Probability

Medium

Core

The probability distribution of a random variable $X$ is

x	0	1	2	3
P(X = x)	$\frac{1}{4}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{2}$

The variance of $X$ is

$\frac{31}{64}$

$\frac{15}{64}$

$\frac{103}{64}$

1

Correct Answer

Option 3

Correct Answer

Explanation

Q30:

2022: 10 Aug Shift 1

Algebra

>

Probability

Medium

Core

A man is known to speak truth 4 out of 5 times. He throws a die and reports that five appears. Then the probability that actual five appears on the dice is

$\frac{3}{8}$

$\frac{4}{9}$

$\frac{5}{9}$

$\frac{5}{8}$

Correct Answer

Option 2

Correct Answer

Explanation

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