Question

In this problem, a fair coin is flipped three times. Assume that a random variable X is defined to be 7 times the number of heads plus 4 times the number of tails.

How many different values are possible for the random variable X?

Answer 1

Solution:

Here a fair coin is flipped three times. So the possible value of number of head in the flipping the coin is 0,1,2 and 3

Let H and T denote number of Head and Tail.

When H = 0, T = 3

When H = 1, T = 2

When H = 2, T = 1

When H = 3, T = 0

Here the random varibale, X = 7H + 4T

When H = 0 and T = 3, X = 7*0 + 4*3 = 12

When H = 1 and T = 2, X = 7*1 + 4*2 = 15

When H = 2 and T = 1, X = 7*2 + 4*1 = 18

When H = 3 and T = 0, X = 7*3 + 4*0 = 21

Hence the possible value of random variable X is 12, 15, 18 and 21.