Find the probability distribution of

number of tails in the simultaneous tosses of three coins.

three coins are tossed simultaneously. Hence, the sample space of the experiment is S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}

X represents the number of tails.

As we see, X is a function on sample space whose range is {0, 1, 2, 3}.

Thus, X is a random variable which can take the values 0, 1, 2 or 3.

P(X = 0) = P(HHH)

P(X = 1) = P(HHT) + P(HTH) + P(THH)

P(X = 2) = P(HTT) + P(THT) + P(TTH)

P(X = 3) = P(TTT)

Hence, the required probability distribution is,