Probability

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

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

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

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

$P, Q$ 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 $R$ i...

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}...

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 exa...

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

In a game, a pair of dice is rolled 24 times. If a person whis the game by not getting 6 on both the dice in any one of the 24 rolls, then the probability that a person wins the game is

The range of a random variable $X$ is $\{0,1,2\}$. If $P(X=0)=3 C^3, P(X=1)=4 C-10 C^2$ and $P(X=2)=5 C-1$, then the value of $C$ is

If four dice are thrown simultaneously, then the probability that none of the dice shows the number 1 on its face, is

If two subsets $A$ and $B$ are selected at random from a set $S$ containing $n$ elements, then the probability that $A \cap B=\phi$ and $A \cup B=S$, is

If eight coins are tossed simultaneously, then the probability of getting atleast six heads is

Bag $B_1$ contains 4 white and 2 black balls. Bag $B_2$ contains 3 white and 4 black balls. A bag is chosen at random and a ball is drawn from it at random, then the probability that the ball drawn is white, is

If $A$ and $B$ are events of a random experiment with $P(A)=0.5, P(B)=0.4$ and $P(A \cap B)=0.3$, then the probability that neither $A$ nor $B$ occurs is

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96 is

A coin is tossed three times. Let $A$ be the event of "getting three heads" and $B$ be the event of "getting a head on the first toss". Then, $A$ and $B$ are

If $P(X=x)=k\left(\frac{3}{8}\right)^x, x=1,2,3 \ldots$ is the probability distribution function of a discrete random variable $X$, then $k=$

From a collection of eight cards numbered 1 to 8 , if two cards are drawn at random, one after the other with replacement, then the probability that the product of numbers that appear on the cards is a perfect square is

Three screws are drawn at random from a lot of 50 screws containing 5 defective ones. Then, the probability of the event that all 3 screws drawn are non-defective, assuming that the drawing is (a) with replacement (b) without replacement re...

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

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

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

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 pr...

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

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

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

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

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 numb...

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 \(x\) 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

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 pa...

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

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

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

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

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

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

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.

Tom and Jerry play a game of alternately
throwing an unfair coin. First one to get head
wins. If Tom starts the game, he has 62.5%
chance of winning the game. Suppose this
coin is tossed 5 times, then the probability of
getting exactly 3 he...

The range of a random variable \(X\) is \(\{1,2,3, \ldots\}\) and \(P(X=x)=\frac{C^x}{x !}\). for \(x=1,2,3\), ... Then, the value of \(C\) is

Box-I contains 3 cards bearing numbers 1, 2, 3 , Box II contains 5 cards bearing numbers 1 , 2, 3, 4, 5 and Box III contains 7 cards bearing numbers 1, 2, 3, 4, 5, 6, 7. One card is drawn at random from each of the boxes. If \(x_i\) be the ...

A coin is tossed until a head appears or it has
been tossed thrice. Given that head doesn’t
appear on the first toss, the probability that
coin tossed thrice 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

A random variable X has the probability distribution

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