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
Your Answer
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)
An urn contains m white and n black balls. A ball is drawn at random and is put back into the urn along with k additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Then the probability that the ball drawn is now white is
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
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
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 and B throw a dice each. The probability that A’s throw is not greater than B’s throw is
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 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
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
Two distinct numbers are selected at random from the first twelve natural numbers. The probability that the sum will be divisible by 3 is
Let A and B be two independent events such that their probabilities are . The probability of exactly one of the events happening is
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 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
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
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
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
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
2n boys are randomly divided into two subgroups containing n boys each. The probability that the two tallest boys are in different groups is
Four numbers are multiplied together. Then the probability that their product will be divisible by 5 or 10 is