Answer to Question #301183 in Statistics and Probability for maih

Question

Four coins are tossed, Let H represent the head and T represent the tail. Let Y be the random variable representing the number of tails that occur. List all the possible outcomes and the corresponding values of the random variable Y

Answer 1

Y=0, when 4 heads occur; {HHHH}

Y=1 , when 1 tail and 3 heads occur; {THHH, HTHH, HHTH, HHHT} 

Y=2, when 2 tails and 2 heads occur;  {TTHH, THTH, THHT, HHTT, HTHT, HTTH}

Y=3, when 3 tails and 1 head occur; {TTTH, TTHT, THTT,HTTT} 

Y=4, when 4 tails occur; {TTTT}

Therefore,

The possible values of the random variable Y are 0, 1, 2, 3, and 4.