CUET Mathematics: AlgebraProbability. Free, no login required.

An alphabet has been selected from English alphabets. What is the probability that it is a vowel given that it precedes 'M' ?

A die is thrown and a coin is tossed. The probability that the outcome will be a number greater than 4 or a head or both is

Let A and B be two independent events. Then which of following statements is not true?

A bag contains 3 white and 2 black balls, another bag contains some white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. If the probability of getting a black ball from the selected bag is 8/15, then the number of white balls in the second bag is

For any two events A and B, which of the following are correct?

(A) $P(A\cup B) = P(A)+P(B)-P(A\cap B)$

(B) $P(A) = P(A\cup B)+P(A\cap B)$

(C) $P(A/B) = P(A)/P(B)$

(D) $P(A) = P(A\cap B)+P(A\cap \bar{B})$

Choose the correct answer from the options given below:

If A and B are two events such that $P(A) \neq 0$, $P(B) \neq 1$ and $P(\bar{A}/\bar{B}) = \frac{1-k}{P(\bar{B})}$, then the value of $k$ is

The mean of the number of heads in a simultaneous toss of three coins is

Three balls are drawn one by one without replacement from a bag containing 5 white and 4 red balls. Let X denote the number of white balls.

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

A company manufactured fans with three units A, B and C. Unit A, B and C produces 2%, 10% and 14% defective fans respectively. Units A, B and C produces 40%, 40% and 20% fans of total products respectively. A fan is randomly chosen that is found to be defective then the probability that the chosen fan is produced from unit C, is

Let A and B are two events associated to a random experiment, then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If E and F are two independent events such that $P(E)=\dfrac{1}{3}, P(F)=\dfrac{3}{5}$, then which of the following is/are correct ?

A. $P(E \cap F) = \dfrac{1}{5}$

B. $P\left(\dfrac{\overline{E}}{F}\right) = \dfrac{2}{3}$

C. $P\left(\dfrac{E}{\overline{F}}\right) = \dfrac{2}{3}$

D. $P\left(\dfrac{E}{F}\right) = \dfrac{2}{3}$

Choose the correct answer from the options given below:

The probability of simultaneous occurrence of at least one of two events E and F is $p$. If the probability that exactly one of E, F occurs is $q$, then $P(\overline{E}) + P(\overline{F})$ is equal to

A pair of coins thrown then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Four cards are drawn successively without replacement from a deck of 52 playing cards. The probability that all the four cards are king is:

A bag contains 5 white, 4 black and 3 red balls. Which of the following statements are True?

A. The probability of drawing three red balls one by one without replacement is $\frac{1}{220}$

B. One by one three balls drawn without replacement then probability that third ball is red is $\frac{1}{4}$

C. The probability of drawing 2 white balls one by one without replacement is $\frac{3}{4}$

D. One by one 3 balls are drawn without replacement then probability that third ball is red is $\frac{3}{4}$

Choose the correct answer from the options given below:

The probability of drawing a one-hundred rupee currency from two boxes one of which contain 3 fifty-rupee currency and 2 one-hundred rupee and other box contain 2 fifty-rupee currency and 3 one-hundred rupee currency notes is-

A pair of unbaised dice is thrown together and sum of the numbers appearing is observed. The probability that the sum of numbers on the dice was 10, given that the observed sum was at least 9, is:

A die is thrown once then,

Match List-I with List-II

Choose the correct answer from the options given below:

A bag contains 4 balls. Let E be an event in which two balls are drawn at random and found to be white, then

Match List-I with List-II

Choose the correct answer from the options given below:

From a lot of 10 items containing 3 defectives, a sample of 4 items is drawn at random. Let X denotes the number of defective items in the sample. If the sample is drawn randomly, then Match List-I with List-II (P(X) denotes the probability of occurence of X)

Choose the correct answer from the options given below:

Suppose that A and B are independent events with $P(A)=\dfrac{1}{7}$ and $P(B)=\dfrac{3}{7}$, then $P(A\cap B)$ is

Given that the events A and B are mutually exclusive such that $P(A)=\dfrac{1}{2}$, $P(A\cup B)=\dfrac{2}{3}$ and $P(B)=p$, then the value of $p$ is:

Let X denotes the number of heads in a simultaneous toss of three coins, then $P(0 < X < 3)$ is

Three students A, B and C can respectively solve 50%, 25% and 20% of the problems in a book. A particular problem is selected at random from the book. The probability that at least one of them will solve the problem is

The probabilities of occurrence of two events E and F are 0.25 and 0.50 respectively. The probability of their simultaneous occurrence is 0.14. The probability that neither E nor F occurs is

A bag contains 4 red and 6 black balls. Two balls are drawn in succession without replacement. The probability that the first is red and the second is black is

The probability distribution of a random variable X is

Match List-I with List-II

Choose the correct answer from the options given below:

If X is a random variable and $a$, $b$ are real numbers, then which of the following statements are true?

(A) $Var(aX+b) = a^2 Var(X)$

(B) $E(aX+b)= a E(X) + b$

(C) $E(aX+b)= a E(X) - E(b)$

(D) $Var(aX+b)= a Var(X) + b$

Choose the correct answer from the options given below:

A random variable X has the following probability distribution:

then, which of the following is correct?

The binomial distribution for which the mean is 5 and variance 4, is