CUET Mathematics - Algebra - Probability | Free Questions - Page 13

Q1:

2022: 10 Aug Shift 1

Algebra

>

Probability

Medium

Core

Five numbers taken out from numbers 1-30 and arrange them in ascending order. The probability that the third number will be 20 is

$\frac{{}^{20}C_2 \times {}^{10}C_2}{{}^{30}C_5}$

$\frac{{}^{19}C_2 \times {}^{10}C_2}{{}^{30}C_5}$

$\frac{{}^{19}C_2 \times {}^{11}C_3}{{}^{30}C_5}$

$\frac{{}^{19}C_2 \times {}^{11}C_2}{{}^{30}C_5}$

Correct Answer

Option 2

Correct Answer

Explanation

Q2:

2022: 10 Aug Shift 1

Algebra

>

Probability

Medium

Core

Bag I contains 4 red and 5 black balls, while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be black. Then the probability that it was drawn from Bag II, is

$\frac{54}{109}$

$\frac{51}{109}$

$\frac{64}{109}$

$\frac{54}{119}$

Correct Answer

Option 1

Correct Answer

Explanation

Q3:

2022: 10 Aug Shift 1

Algebra

>

Probability

Easy

Core

A card is picked at random from a pack of 52 playing cards. If the picked card is a queen, then probability of card to be of spade type also, is

$\frac{1}{3}$

$\frac{4}{13}$

$\frac{1}{4}$

$\frac{1}{2}$

Correct Answer

Option 3

Correct Answer

Explanation

Q4:

2022: 30 Aug Shift 1

Algebra

>

Probability

Easy

Core

Two numbers are selected at random (without replacement) from the first three positive integers. Let $X$ denotes the larger of the two integers, then the probability distribution of $X$ is

$x$	2	3
$P(X=x)$	1/3	2/3

$x$	2	3
$P(X=x)$	1/2	1/2

$x$	2	3
$P(X=x)$	2/3	1/3

$x$	2	3
$P(X=x)$	1/5	4/5

Correct Answer

Option 1

Correct Answer

Explanation

Q5:

2022: 30 Aug Shift 1

Algebra

>

Probability

Easy

Core

The probability distribution of number of doublets in three throws of a pair of dice is

$x$	0	1	2	3
$P(X=x)$	125/216	75/216	15/216	1/216

$x$	0	1	2	3
$P(X=x)$	75/216	125/216	1/216	15/216

$x$	0	1	2	3
$P(X=x)$	1/216	75/216	15/216	125/216

$x$	0	1	2	3
$P(X=x)$	1/216	15/216	75/216	125/216

Correct Answer

Option 1

Correct Answer

Explanation

Q6:

2022: 30 Aug Shift 1

Algebra

>

Probability

Medium

Core

Three urns contain 6 red, 4 black; 4 red, 6 black and 5 red, 5 black marbles respectively. One of the urns is selected at random and a marble is drawn from it. If the marble drawn is red, then the probability that it is drawn from the first urn is

$\frac{6}{10}$

$\frac{4}{10}$

$\frac{5}{10}$

$\frac{2}{5}$

Correct Answer

Option 4

Correct Answer

Explanation

Q7:

2022: 30 Aug Shift 1

Algebra

>

Probability

Medium

Core

Three persons A, B and C were given a task, whose probabilities of completion their task on time are $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. They were asked to complete the task on time independently.

The probability that exactly one of them complete the task on time is

$\frac{2}{15}$

$\frac{2}{5}$

$\frac{3}{20}$

$\frac{13}{20}$

Correct Answer

Option 4

Correct Answer

Explanation

Q8:

2022: 30 Aug Shift 1

Algebra

>

Probability

Medium

Core

Three persons A, B and C were given a task, whose probabilities of completion their task on time are $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. They were asked to complete the task on time independently.

The probability that exactly two of them complete the task on time is

$\frac{3}{20}$

$\frac{13}{30}$

$\frac{1}{5}$

$\frac{2}{15}$

Correct Answer

Option 1

Correct Answer

Explanation

Q9:

2022: 30 Aug Shift 1

Algebra

>

Probability

Easy

Core

Three persons A, B and C were given a task, whose probabilities of completion their task on time are $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. They were asked to complete the task on time independently.

The probability that B alone complete the task on time is:

$\frac{13}{30}$

$\frac{3}{20}$

$\frac{2}{5}$

$\frac{2}{15}$

Correct Answer

Option 4

Correct Answer

Explanation

Q10:

2022: 30 Aug Shift 1

Algebra

>

Probability

Easy

Core

Three persons A, B and C were given a task, whose probabilities of completion their task on time are $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. They were asked to complete the task on time independently.

The probability that the task is completed on time by none of them is

$\frac{3}{20}$

$\frac{2}{5}$

$\frac{13}{30}$

$\frac{2}{15}$

Correct Answer

Option 2

Correct Answer

Explanation

Q11:

2022: 30 Aug Shift 1

Algebra

>

Probability

Easy

Core

Three persons A, B and C were given a task, whose probabilities of completion their task on time are $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. They were asked to complete the task on time independently.

The probability that task is completed on time by at least one of them is:

$\frac{2}{5}$

$\frac{3}{20}$

$\frac{3}{5}$

$\frac{2}{15}$

Correct Answer

Option 3

Correct Answer

Explanation

Q12:

2022: 16 July Shift 2

Algebra

>

Probability

Easy

Core

Let X be the random variable with probability distribution given by the following table.

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

The value of $P(X \leq 1)$ is:

$\frac{3}{8}$

$\frac{3}{4}$

$\frac{1}{4}$

$\frac{1}{2}$

Correct Answer

Option 4

Correct Answer

Explanation

Q13:

2022: 16 July Shift 2

Algebra

>

Probability

Easy

Core

A random variable X has the following probability distribution:

x	1	2	3	4
p(x)	2k	4k	3k	k

The value of E(X) is:

0.23

0.1

1.6

2.3

Correct Answer

Option 4

Correct Answer

Explanation

Q14:

2022: 16 July Shift 2

Algebra

>

Probability

Easy

Core

CASE STUDY

In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let $\frac{3}{5}$ be the probability that he knows the answer and $\frac{2}{5}$ be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability $\frac{1}{3}$ . Let $E_1$ , $E_2$ , and E be the events that the student knows the answer, guesses the answer and answers correctly respectively. A student answers correctly if he/she knows the answer. Using the above information, answer the question:

The value of $P(E/E_1)$ is

$\frac{1}{3}$

1

$\frac{2}{3}$

$\frac{4}{5}$

Correct Answer

Option 2

Correct Answer

Explanation

Q15:

2022: 16 July Shift 2

Algebra

>

Probability

Medium

Core

CASE STUDY

In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let $\frac{3}{5}$ be the probability that he knows the answer and $\frac{2}{5}$ be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability $\frac{1}{3}$ . Let $E_1$ , $E_2$ , and E be the events that the student knows the answer, guesses the answer and answers correctly respectively. A student answers correctly if he/she knows the answer. Using the above information, answer the question:

The value of $P(E)$ is

$\frac{11}{15}$

$\frac{4}{15}$

$\frac{1}{5}$

1

Correct Answer

Option 1

Correct Answer

Explanation

Q16:

2022: 16 July Shift 2

Algebra

>

Probability

Easy

Core

CASE STUDY

In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let $\frac{3}{5}$ be the probability that he knows the answer and $\frac{2}{5}$ be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability $\frac{1}{3}$ . Let $E_1$ , $E_2$ , and E be the events that the student knows the answer, guesses the answer and answers correctly respectively. A student answers correctly if he/she knows the answer. Using the above information, answer the question:

The probability that a question is guessed by a student and found to be correct is.

$\frac{1}{5}$

$\frac{2}{15}$

$\frac{4}{15}$

$\frac{2}{5}$

Correct Answer

Option 2

Correct Answer

Explanation

Q17:

2022: 16 July Shift 2

Algebra

>

Probability

Medium

Core

CASE STUDY

In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let $\frac{3}{5}$ be the probability that he knows the answer and $\frac{2}{5}$ be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability $\frac{1}{3}$ . Let $E_1$ , $E_2$ , and E be the events that the student knows the answer, guesses the answer and answers correctly respectively. A student answers correctly if he/she knows the answer. Using the above information, answer the question:

The probability of 'the student knows the answer given that he answered it correctly' is

$\frac{2}{11}$

$\frac{5}{3}$

$\frac{9}{11}$

$\frac{3}{13}$

Correct Answer

Option 3

Correct Answer

Explanation

Q18:

2022: 16 July Shift 2

Algebra

>

Probability

Medium

Core

CASE STUDY

In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let $\frac{3}{5}$ be the probability that he knows the answer and $\frac{2}{5}$ be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability $\frac{1}{3}$ . Let $E_1$ , $E_2$ , and E be the events that the student knows the answer, guesses the answer and answers correctly respectively. A student answers correctly if he/she knows the answer. Using the above information, answer the question:

It is given that student marked the answer correctly, the probability that he guesses is

$\frac{3}{5}$

$\frac{2}{15}$

$\frac{11}{15}$

$\frac{2}{11}$

Correct Answer

Option 4

Correct Answer

Explanation

Q19:

2022: 23 Aug Shift 1

Algebra

>

Probability

Easy

Core

If a fair coin is tossed 10 times, then the probability of getting all heads or all tails, is :

$\frac{1}{2}$

$\frac{1}{2^{10}}$

$\frac{5}{2^9}$

$\frac{1}{2^9}$

Correct Answer

Option 4

Correct Answer

Explanation

Q20:

2022: 23 Aug Shift 1

Algebra

>

Probability

Medium

Core

If an unbiased coin is tossed 10 times, probability of obtaining more head than tail is :

$\frac{63}{256}$

$\frac{63}{512}$

$\frac{193}{512}$

$\frac{193}{256}$

Correct Answer

Option 3

Correct Answer

Explanation

Q21:

2022: 23 Aug Shift 1

Algebra

>

Probability

Hard

Core

Consider an experiment of tossing 3 coins simultaneously. Define the following events:

$E$ = [Three heads or three tails appear]

$F$ = [At least two heads appear] and

$G$ = [At most two heads appear]

Choose the correct option:

E and G are independent events

E and F are independent events

F and G are independent events

E and F are dependent events

Correct Answer

Option 2

Correct Answer

Explanation

Q22:

2022: 23 Aug Shift 1

Algebra

>

Probability

Medium

Core

In the family mother, father and son stand up at random for a family picture. Define following two events :

$E$ = [Son stands at one of the two ends in the picture]

$F$ = [Father stands in the middle of the picture]

The value of $P(F/E)$ is :

$1$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{1}{9}$

Correct Answer

Option 3

Correct Answer

Explanation

Q23:

2022: 23 Aug Shift 1

Algebra

>

Probability

Hard

Core

These days competitive examinations are held in online mode. During the examination student either guesses or copies or knows the answer of a multiple choice question (MCQ) with four choices each. The probability that a student makes guesses is $\frac{1}{3}$ and that he/she copies $\frac{1}{6}$ . The probability of marking answer correctly when he/she copied is $\frac{1}{8}$ and probability of making answer correctly when he/she guesses is $\frac{1}{4}$ . It is also assumed that a student marked answer correctly if he/she knows the answer.

By using the above mentioned information answer following question.

The probability that a student knows the answer, is:

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{5}{6}$

$1$

Correct Answer

Option 2

Correct Answer

Explanation

Q24:

2022: 23 Aug Shift 1

Algebra

>

Probability

Hard

Core

These days competitive examinations are held in online mode. During the examination student either guesses or copies or knows the answer of a multiple choice question (MCQ) with four choices each. The probability that a student makes guesses is $\frac{1}{3}$ and that he/she copies $\frac{1}{6}$ . The probability of marking answer correctly when he/she copied is $\frac{1}{8}$ and probability of making answer correctly when he/she guesses is $\frac{1}{4}$ . It is also assumed that a student marked answer correctly if he/she knows the answer.

By using the above mentioned information answer following question.

If answer is correct, the probability that he guesses, is :

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{1}{8}$

$\frac{1}{3}$

Correct Answer

Option 1

Correct Answer

Explanation

Q25:

2022: 23 Aug Shift 1

Algebra

>

Probability

Hard

Core

These days competitive examinations are held in online mode. During the examination student either guesses or copies or knows the answer of a multiple choice question (MCQ) with four choices each. The probability that a student makes guesses is $\frac{1}{3}$ and that he/she copies $\frac{1}{6}$ . The probability of marking answer correctly when he/she copied is $\frac{1}{8}$ and probability of making answer correctly when he/she guesses is $\frac{1}{4}$ . It is also assumed that a student marked answer correctly if he/she knows the answer.

By using the above mentioned information answer following question.

The conditional probability that his answer is correct when it is given that he knew it :

$\frac{1}{2}$

$0$

$1$

$\frac{1}{4}$

Correct Answer

Option 3

Correct Answer

Explanation

Q26:

2022: 23 Aug Shift 1

Algebra

>

Probability

Hard

Core

These days competitive examinations are held in online mode. During the examination student either guesses or copies or knows the answer of a multiple choice question (MCQ) with four choices each. The probability that a student makes guesses is $\frac{1}{3}$ and that he/she copies $\frac{1}{6}$ . The probability of marking answer correctly when he/she copied is $\frac{1}{8}$ and probability of making answer correctly when he/she guesses is $\frac{1}{4}$ . It is also assumed that a student marked answer correctly if he/she knows the answer.

By using the above mentioned information answer following question.

The probability of answering a question correctly, is :

$\frac{8}{11}$

$\frac{1}{5}$

$\frac{29}{48}$

$\frac{5}{29}$

Correct Answer

Option 3

Correct Answer

Explanation

Q27:

2022: 23 Aug Shift 1

Algebra

>

Probability

Hard

Core

These days competitive examinations are held in online mode. During the examination student either guesses or copies or knows the answer of a multiple choice question (MCQ) with four choices each. The probability that a student makes guesses is $\frac{1}{3}$ and that he/she copies $\frac{1}{6}$ . The probability of marking answer correctly when he/she copied is $\frac{1}{8}$ and probability of making answer correctly when he/she guesses is $\frac{1}{4}$ . It is also assumed that a student marked answer correctly if he/she knows the answer.

By using the above mentioned information answer following question.

The probability that he copied it given that his answer is correct :

$\frac{24}{29}$

$\frac{1}{29}$

$\frac{4}{29}$

$\frac{6}{29}$

Correct Answer

Option 2

Correct Answer

Explanation

Q28:

2022: 25 May Shift 1

Algebra

>

Probability

Easy

Common

In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Then, E (X) is :

$\frac{7}{10}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{7}{11}$

Correct Answer

Option 1

Correct Answer

Explanation

Q29:

2022: 25 May Shift 1

Algebra

>

Probability

Easy

Common

In a box containing 100 bulbs, 10 are defective. Then the probability, that out of a sample of 5 bulbs none is defective, is:

$10^{-1}$

$\left(\frac{1}{2}\right)^5$

$\left(\frac{9}{10}\right)^5$

$\left(\frac{9}{10}\right)$

Correct Answer

Option 3

Correct Answer

Explanation

Q30:

2022: 25 May Shift 1

Algebra

>

Probability

Easy

Core

Two dice are thrown simultaneously. If X denotes the number of sixes, then the variance of X is:

$\frac{5}{18}$

$\frac{7}{18}$

$\frac{1}{3}$

$\frac{2}{3}$

Correct Answer

Option 1

Correct Answer

Explanation

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