On a multiple choice examination with three possible answers (out of which only one is correct) for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

A card form a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn at random and are found to be both clubs. Find  the probability of the lost card being of clubs.

From a lot of 10 bulbs, which includes 3 defectives, a sample of 2 bulbs is drawn at random. Find the probability distribution of the number of defective bulbs.

Probabilities of solving problem independently by A and B are $\frac{1}{2}$ and $\frac{1}{3}$respectively. If both try to solve the problem independently, find the probability that

(i) the problem is solved

(ii) exactly one of them solves the problem.

Suppose 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.

How many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%?

A girl throws a die. If she get a 5 OR 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 OR 4, she tosses a coin two times and notes the number of heads obtained. If she obtained exactly two heads, what is the probability that she threw 1, 2, 3 OR 4 with the die?

If  the coefficient of x is in expansion of ${\left({\mathrm{x}}^2 + \frac{\mathrm{k}}{\mathrm{x}}\right)}^5$ is 270, then k is equal to

• 1

• 2

• 3

• 4

3 out of 6 vertices of a regular hexagon are chosen at a time at random. The probability that the triangle formed with these three vertices is an equilateral triangle, is

• $\frac{1}{2}$

• $\frac{1}{5}$

• $\frac{1}{10}$

• $\frac{1}{20}$

If 12 identical balls are to be placed in 3 identical boxes, then the probability that  one of the boxes contains exactly 3 balls, is