An anti–aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probability of hitting the plane at the first shot, 2^nd, 3^rd and 4^th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability of A and B being selected is at most 0.3. Is it possible that the probability of B being selected is 0.9?

Cards are drawn one by one at random from a well shuffled pack of 52 playing cards until 2 aces are drawn for the first time. If N is the number of cards required to be drawn show that
 where 2 < n ≤ 50

If A, B, C be events such that P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(AB) = 0.08, P(AC) = 0.28, P(ABC) = 0.09 and P(A ∪ B ∪ C) ≥ 0.75, then show that P(BC) lies in the interval [0.23, 0.48].

A and B are independent events. The probability that both A and B occur is  and probability that neither of them occur is . Find the probability of the occurrence of A.

In a city only two news papers A and B are published. It is known that 25% of the city population read A and 20% read B, while 8% read A and B. It is also known that 30% of those who read A but not B and 40% of those who read B but not A look into the advertisement. 50% of those who read both A and B look into the advertisement. What is the percentage of the population that reads an advertisement?

In a multiple choice question there are four alternative answers out of which one or more is correct. A candidate will get full marks in the question only if he ticks the correct answers. If he is allowed up to three chances to answer the question, find the probability that he will get marks in the question?

A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point.

A box contains two 50 paise coins, 5 twenty five paise coins and a certain number N(≥ 2) of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these coins is less than one rupee and 50 paise.

Suppose the probability for A winning a game against B is 0.4. If A has an option of playing either a best of 3 games or best of 5 games match against B, which option should he choose so that the probability of his winning the match is higher.

Let A be a set containing n elements. A subset P of A is constructed at random. The set A is reconstructed by replacing the elements of P. A subset of Q of A is again chosen at random. Find the probability that P and Q have no elements in common.

4 five rupee coins, 3 two rupee coins and 2 one rupee coins are stacked together in a column at random. The probability that the coins of the same denomination are consecutive, is

a)

b)

c)

d) None of these

Let x =. The index n is given a positive integral value at random. The probability that the value of x will have 3 in the unit’s place, is

a)

b)

c)

d) None of these

Three different numbers are selected at random from the set A = {1, 2, 3, .  .  . , 10}. The probability that the product of two of the numbers is equal to the third is

a)

b)

c)

d) None of these

The probability that out of 10 persons, all born in April, at least two have the same birthday, is

a)

b)

c)

d)

A point is selected at random from the interior of the circle. The probability that the point is closer to the centre than the boundary of the circle, is

a)

b)

c)

d) None of these

There are n persons sitting in a row. Two of them are selected at random. The probability that two selected persons are not together, is

a)

b)

c)

d)

An elevator starts with m passengers and stops at n floors (m ≤ n). The probability that no two passengers alight at the same floor, is

a)

b)

c)

d)

Two integers x and y are chosen with replacement out of the set {0, 1, 2, 3, .  .  .  .10}. Then, the probability that |x – y| > 5, is

a)

b)

c)

d)

The probability that when 12 balls are distributed among three boxes, the first will contain three balls is

a)

b)

c)

d) None of these

There is a five volume dictionary among 50 books arranged on a shelf in a random order. If the volumes are not necessarily kept side by side, the probability that they occur in increasing order from left to right, is

a)

b)

c)

d)

Three persons A, B, C are to speak at a function along with five others. If they all speak in random order, the probability that A speaks before B and B speaks before C is

a)

b)

c)

d) None of these

Let A and B be two independent events such that . Then,  is equal to

a)

b)

c)

d) None of these