Question 1

(a)When a balanced dime is tossed four times, sixteen equally likely outcomes are possible. Here, for

instance, HHTH means that the first two tosses are heads, the third is tails and fourth results again in

head. Let X denote the total number of heads obtained in the four tosses. Then X is a random variable.

i. List all possible outcomes of four tosses of a coin.

ii. Determine whether the random variable is discrete or continuous and what possible values can be

taken by the random variable X.

iii. Find the probability distribution of X.

iv. Find the average number of heads that can be obtained in four tosses of a dime..

(b) A lot of 100 light bulbs is inspected using the following procedure:

Five bulbs are chosen at random and tested. If all five light up, the entire lot is accepted. Suppose a lot

contains 20 defective bulbs. What is the probability that the lot will get accepted?