Probability practice · Mixed difficulty

Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a women is

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

The mean and variance of a binomial distribution are 4 and 3 respectively, then the probability of getting exactly six successes in this distribution is

In a school there are 100 students 60 of them don't like Chocolate and 50 don't like Biscuit and 10 of them like none then how many of them like both?

From a pack of cards two are accidently dropped. Probability that they are of opposite shade is

Three dice are thrown together. The probability that the sum of the numbers appearing on them is 9 , is

An unbiased cubical die is thrown 5 times. The probability that the maximum number appearing on the die is 4 is

A parents has two children. If one of them is boy, then the probability that other is, also a boy, is

If the mean of a binomial distribution with 9 trials is 6, then its variance is

A box ' $A$ ' contanis 2 white, 3 red and 2 black balls. Another box ' $B$ ' contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box ' $B$ ' is

There are $n$ stations between two cities $A$ and $B$. A train is to stop at three of these $n$ stations. What is the probability that no two of these three stations are consecutive?

A bag contains 4 brown and 5 white balls. A man pulls two balls at random without replacement. The probability that the man gets both the balls of the same colour is

If $\frac{1}{4}(1+4 p), \frac{1}{4}(1-p)$ and $\frac{1}{2}(1-2 p)$ are the probabilities of three mutually exclusive events, then $2 p$ is

If $A$ and $B$ are two events. The probability that at most one of $A, B$ occurs, is

A class contains 20 boys and 20 girls of which half the boys and half the girls have cat eyes. If one student is selected from the class & if the probability that either the student is a boy or has cat eyes is $\frac{{a}}{{b}}$, then $\sqrt{{a}^2+{b}^2}=$

The probability of choosing a number divisible by 6 or 8 from among 1 to 90 is

An urn contains 3 red and 5 blue balls. The probability that two balls are drawn in which 2nd ball drawn is blue without replacement, is

$A$ and $B$ are are two events. Odds against $A$ are 2 to 1 and odds in favour of $A \cup B$ are 3 to1. If $x \le P\left( B \right) \le y$, then ordered pair $\left( {x,y} \right)$ is

One hundred identical coins, each with probability, p, of showing up heads are tossed once. If $0 < p < 1,$ and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of $p,$ is

A box contains 3 white and 2 red balls. If we draw one ball and without replacing the first ball, the probability of drawing red ball in the second draw is

A car is parked by an owner amongst 25 cars in a row, not at either end. On his return he finds that exactly 15 places are still occupied. The probability that both the neighboring places are empty is

A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is

In a binomial distribution, the mean is 4 and variance is 3. Then, its mode is

The probability of obtaining an even prime number on each die when a pair of dice is rolled is

An urn contains 6 white and 4 black balls. A fair die is rolled and that number of balls are chosen from the urn. The probability that the balls selected are white is

An almirah stores 5 black and 4 white socks well mixed. A boy pull out 2 socks at random. The probability that 2 are of the same colour is

If the letters of the word ‘REGULATION’ be arranged at random, the probability that there will be exactly 4 letters between $R$ and $E$ is

If three integers are chosen at random from the set of first 20 natural numbers, the chance that their product is a multiple of 3 , is

$A$ is a set containing $n$ elements. A subset $P$ of $A$ is chosen at random. The set $A$ is reconstructed by replacing the elements of $P$. A subset $Q$ is again chosen at random. The probability that $P \cup Q$ contains just one element, is

On a Saturday night $20 \%$ of all drives in U.S.A. are under the influence of alcohol. The probability that a driver under the influence of alcohol will have an accident is $0.001.$ The probability that a sober driver will have an accident is $0.0001.$ If a car on a Saturday night smashed into a tree, the probability that the driver was under the influence of alcohol is