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,


X



0



1



2



3



P(X)



1/8



3/8



3/8



1/8



4
1