Question

Let X represent the difference between the number of heads and the number of tails when a coin is tossed 6 times. What are the possible values of X?

Answer 1

A coin is tossed 6 times and X represents the difference between the number of heads and the number of tails.

Sample space of the experiment is

S = {(0 heads, 6 tails), (1 head, 5 tails), (2 heads, 4 tails), (3 heads, 3 tails), (4 heads, 2 tails), (5 heads, 1 tail), (6 heads, 0 tails)}

The values of X corresponding to these outcomes are as follows:

∴  X(0 heads, 6 tails) = 0 – 6 = – 6

X(1 head, 5 tails) = 1 – 5 = – 4

X(2 heads, 4 tails) = 2 – 4 = – 2

X(3 heads, 3 tails) = 3 – 3 = 0

X(4 heads, 2 tails) = 4 – 2 = 2

X(5 heads, 1 tail) = 5 – 1 = 4

X(6 heads, 0 tails) = 6 – 0 = 6

∴ Possible values of X are {– 6, – 4, –2, 0, 2, 4, 6}.