Probability · Mathematics · AP EAPCET

S is the sample space and $A, B$ are two events of a random experiment. Match the items of List $A$ with the items of List B

The probability of getting a sum 9 when two dice are thrown is

If $$A$$ and $$B$$ are two events such that $$P(B) \neq 0$$ and $$P(B) \neq 1$$, then $$P(\bar{A} \mid \bar{B})$$ is

Two brothers $$X$$ and $$Y$$ appeared for an exam. Let $$A$$ be the event that $$X$$ has passed the exam and $$B$$ is the event that $$Y$$ has passed. The probability of $$A$$ is $$\frac{1}{7}$$ and of $$B$$ is $$\frac{2}{9}$$. Then, the probability that both of them pass the exam is

A bag contains 4 red and 3 black balls. A second bag contains 2 red and 3 black balls. One bag is selected at random. If from the selected bag, one ball is drawn at random, then the probability that the ball drawn is red, is

In a Binomial distribution, if '$$n$$' is the number of trials and the mean and variance are 4 and 3 respectively, then $$2^{32} p\left(X=\frac{n}{2}\right)=$$

For a Poisson distribution, if mean $$=l$$, variance $$=m$$ and $$l+m=8$$, then $$e^4[1-P(X>2)]=$$

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked randomly. The probability that it is neither red nor green is

For two events $$A$$ and $$B$$, a true statement among the following is

Five digit numbers are formed by using digits $$1,2,3,4$$ and 5 without repetition. Then, the probability that the randomly chosen number is divisible by 4 is

A manager decides to distribute ₹ 20000 between two employees $$X$$ and $$Y$$. He knows $$X$$ deserves more than $$Y$$, but does not know how much more. So, he decides to arbitrarily break ₹ 20000 into two parts and give $$X$$ the bigger part. Then, the chance that $$X$$ gets twice as much as $$Y$$ or more is

Which of the following is not a property of a Binomial distribution?

In a Binomial distribution $$B(n, p)$$, if the mean and variance are 15 and 10 respectively, then the value of the parameter $$n$$ is

A box contains 100 balls, numbered from 1 to 100 . If 3 balls are selected one after the other at random with replacement from the box, then the probability that the sum of the three numbers on the balls selected from the box is an odd number, is

In a lottery, containing 35 tickets, exactly 10 tickets bear a prize. If a ticket is drawn at random, then the probability of not getting a prize is

A bag contains 7 green and 5 black balls. 3 balls are drawn at random one after the other. If the balls are not replaced, then the probability of all three balls being green is

If $$x$$ is chosen at random from the set $$\{1,2,3, 4\}$$ and $$y$$ is chosen at random from the set $$\{5,6,7\}$$, then the probability that $$x y$$ will be even is

The discrete random variables $$X$$ and $$Y$$ are independent from one another and are defined as $$X \sim B(16,0.25)$$ and $$Y \sim P(2)$$. Then, the sum of the variance of $$X$$ and $$Y$$ is

If 6 is the mean of a Poisson distribution, then $$P(X \geq 3)=$$

One card is selected at random from 27 cards numbered form 1 to 27. What is the probability that the number on the card is even or divisible by 5.

Nine balls one drawn simultaneously from a bag containing 5 white and 7 black balls. The probability of drawing 3 white and 6 black balls is

The probabilities that $$A$$ and $$B$$ speak truth are $$\frac{4}{5}$$ and $$\frac{3}{4}$$ respectively. The probability that they contradict each other when asked to speak on a fact is

The mean and variance of a binomial variable X are 2 and 1 respectively. The probability that X takes values greater than 1 is

P speaks truth in 70% of the cases and Q in 80% of the cases. In what percent of cases are they likely to agree in stating the same fact

If $$A$$ and $$B$$ are two events with $$P(A \cap B)=\frac{1}{3}, P(A \cup B)=\frac{5}{6}$$ and $$P\left(A^C\right)=\frac{1}{2}$$, then the value of $$P\left(B^C\right)$$ is

A coin is tossed 2020 times. The probability of getting head on 1947th toss is

A discrete random variable X takes values 10, 20, 30 and 40. with probability 0.3, 0.3, 0.2 and 0.2 respectively. Then the expected value of X is

Let $$X$$ be a random variable which takes values $$1,2,3,4$$ such that $$P(X=r)=K r^3$$ where $$r=1,2,3,4$$ then

12 balls are distributed among 3 boxes, then the probability that the first box will contain 3 balls is

A random variable X has the probability distribution

For the events E = {X is a prime number} and F = {X < 4}, then P(E $$\cup$$ F) is

A die is tossed thrice. If event of getting an even number is a success, then the probability of getting at least 2 successes is