Question

Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in its inverse images

Answer 1

Let X is the random variable that denotes the number of tails when three coins are tossed simultaneously.

Sample space S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

∴ ‘X’ takes the values 0, 1, 2, 3

i.e., (HHH) = 0 

X(HHT, HTH, THH) = 1 

X(HTT, THT, TTH) = 2 

X(TTT) = 3

Values of the random variable	0	1	2	3	Total
Number of elements in inverse image	1	3	3	1	8