Probability · Mathematics · AP EAPCET

Two natural numbers are chosen at random from 1 to 100 and are multiplied. If $A$ is the event that the product is an even number and $B$ is the event that the product is divisible by 4 , then $P(A \cap \bar{B})=$

A box $P$ contains one white ball, three red ball and two black balls. Another box $Q$ contains two white balls, three red balls and four black balls. If one ball is drawn at random from each one of the two boxes, then the probability that the balls drawn are of different colour is

A person is known to speak false once out of 4 times, If that person picks a card at random from a pack of 52 cards and reports that it is a king, then the probability that it is actually a king is

For a binomial variate $X \sim B(n, p)$ the difference between the mean and variance is 1 and the difference between their square is 11 . If the probability of $P(x=2)=m\left(\frac{5}{6}\right)^n$ and $n=36$, then $m: n$

The probability that a man failing to hit a target is $\frac{1}{3}$. If he fires 4 times, then the probability that he hits the target at least thrice is

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

$$ \text { List A } $$		$$ \text { List B } $$
I	$A, B$ are mutually exclusive events	a.	$$ P(A \cap B)=P(B)-P(\bar{A}) $$
II	$$ A, B \text { are independent events } $$	b.	$$ P(A) \leq P(B) $$
III	$$ A \cap B=A $$	c.	$$ P\left(\frac{\bar{A}}{B}\right)=1-P(A) $$
IV	$$ A \cup B=S $$	d.	$$ P(A \cup B)=P(A)+P(B) $$
		e.	$$ P(A)+P(B)=2 $$

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

Two digits are selected at random from the digits 1 through 9. If their sum is even, then the probability that both are odd, is

A, B and C are mutually exclusive and exhaustive events of a random experiment and $E$ is an event that occurs in conjunction with one of the events $\mathrm{A}, \mathrm{B}$ and $C$. The conditional probabilities of $E$ given the happening of $A, \mathrm{~B}$ and C are respectively $0.6,0.3$ and 0.1. If $P(A)=0.30$ and $P(B)=0.50$, then $P(C / E)=$

For the probability distribution of a discrete random variable $X$ as given below, then mean of $X$ is

X = x	-2	-1	0	1	2	3
P(X = x)	$$ \frac{1}{10} $$	$$ K+\frac{2}{10} $$	$$ K+\frac{3}{10} $$	$$ K+\frac{3}{10} $$	$$ K+\frac{4}{10} $$	$$ K+\frac{2}{10} $$

In a random experiment, two dice are thrown and the sum of the numbers appeared on them is recorded. This experiment is repeated 9 times. If the probability that a sum of 6 appears atleast once is $P_1$ and a sum of 8 appears atleast once is $P_2$, then $P_1: P_2=$

If 7 different balls are distributed among 4 different boxes, then the probability that the first box contains 3 balls is

Out of first 5 consecutive natural numbers, if two different numbers $x$ and $y$ are chosen at random, then the probability that $x^4-y^4$ is divisible by 5 is

A bag contains 2 white, 3 green and 5 red balls. If three balls are drawn one after the other without replacement, then the probability that the last ball drawn was red is

There are 2 bags each containing 3 white and 5 black balls and 4 bags each containing 6 white and 4 black balls. If a ball drawn randomly from a bag is found to be black, then the probability that this ball is from the first set of bags is

If two cards are drawn randomly from a pack of 52 playing cards, then the mean of the probability distribution of number of kings is

In a consignment of 15 articles, it is found that 3 are defective. If a sample of 5 articles is chosen at random from it, then the probability of having 2 defective articles is

If 5 letters are to be placed in 5 -addressed envelopes, then the probability that atleast one letter is placed in the wrongly addressed envelope, is

A student writes an examination which contains eight true of false questions. If he answers six or more questions correctly, the passes the examination. If the student answers all the questions, then the probability that he fails in the examination, is

The probabilities that a person goes to college by car is $\frac{1}{5}$, by bus is $\frac{2}{5}$ and by train is $\frac{3}{5}$, respectively. The probabilities that he reaches the college late if he takes car, bus and train are $\frac{2}{7}, \frac{4}{7}$ and $\frac{1}{7}$, respectively, If he reaches the college on time, then probability that he travelled by car is

$P, Q$ and $R$ try to hit the same target one after the other. If their probabilities of hitting the target are $\frac{2}{3}, \frac{3}{5}, \frac{5}{7}$ respectively, then the probability that the target is his by $P$ or $Q$ but not by $R$ is

A box contains $20 \%$ defective bulbs. Five bulbs are chosen randomly from this box. Then, the probability that exactly 3 of the chosen bulbs are defective, is

If a random variable $X$ satisfies poisson distribution with a mean value of 5 , then probability that $X<3$ is

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