Pal’s gardener is not dependable, the probability that he will forget to water the rose bush is 2/3 The rose bush is in questionable condition. Anyhow if watered, the probability of its withering is 1/2, if not watered, the probability of its withering is ¾. Pal went out of station and on returning, he finds that the rose bush has withered. Then the chance that the gardener did not water the bush is

a)

b)

c)

d)

A box contains N coins, m of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is , while it is  when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. Then the probability that the coin drawn is fair is

a)

b)

c)

d)

For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the first exam is p. If he fails in one of the exams, then the probability of his passing in the next exam is ., otherwise it remains the same. Then the probability that he will qualify is

a) 2p² – p

b) 2p² – 2p

c) 2p² – p³

d) None of these

A is targeting to hit B, B and C are targeting to hit A. Probability of hitting the target by A, B and C are  respectively. If A is hit then the probability that B hits the target and C does not is

a)

b)

c)

d) None of these

A is one of 6 horses entered for a race, and is to be ridden by one of the two jockeys B and C. It is 2 to 1 that B rides A, in which case all the horses are equally likely to win. If C rides A, his chance of winning is trebled. What are the odds against winning of A?

a) 5 : 13

b) 5 : 18

c) 13 : 5

d) None of these

A and B throw a dice each. The probability that A’s throw is not greater than B’s throw is

a)

b)

c)

d)

If the sides of a triangle are decided by the throw of a single dice thrice, the probability that the triangle is of maximum area given that it is an isosceles triangle is

a)

b)

c)

d) None of these

A second order determinant is written down at random using the numbers 1, −1, as elements. The probability that the value of the determinants is non zero is

a)

b)

c)

d)

10 different books and 2 different pens are given to 3 boys so that each gets equal number of things. The probability that the same boy does not receive both the pens is

a)

b)

c)

d)

Two distinct numbers are selected at random from the first twelve natural numbers. The probability that the sum will be divisible by 3 is

a)

b)

c)

d) None of these

Let A and B be two independent events such that their probabilities are . The probability of exactly one of the events happening is

a)

b)

c)

d) None of these

A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is

a)

b)

c)

d) None of these

A coin is tossed n times. The probability of getting at least one head is greater than that of getting at least two tails by . Then n is

a) 5

b) 10

c) 15

d) None of these

A man firing at a distant target has a10% chance of hitting the target in one shot. The number of times he must fire at the target to have at least 50% chance of hitting the target is

a) 11

b) 9

c) 7

d) 5

The numbers 1, 2, 3, .  .  ., n are arranged in a random order. The probability that the digits 1, 2, 3, .  .  .k (k < n) appears as neighbours in that order is

a)

b)

c)

d) None of these

The numbers 1, 2, 3, .  .  ., n are arranged in a random order. The probability that the digits 1, 2, 3, .  .  .k (k < n) appear as neighbours is

a)

b)

c)

d)

Given that the sum of two non-negative quantities is 200, the probability that their product is not less than  times their greatest product value is

a)

b)

c)

d)

The probability of the simultaneous occurrence of two events A and B is p. If the probability that exactly one of A, B occurs is q then show that

For two events A and B it is given that
 
then show that A and B are independent events and

If the independent events A and B are such that 0 < P (A) < 1 and 0 < P (B) < 1 then A and  are independent

a) True

b) False

If the independent events A and B are such that 0 < P (A) < 1 and 0 < P (B) < 1 then  and  are independent

a) True

b) False

2n boys are randomly divided into two subgroups containing n boys each. The probability that the two tallest boys are in different groups is

a)

b)

c)

d) None of these

Four numbers are multiplied together. Then the probability that their product will be divisible by 5 or 10 is

a)

b)

c)

d)