Q4 of 105 Page 569

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



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