Q. 45.0( 5 Votes )

A coin is tossed three times, if head occurs on first two tosses, find the probability of getting head on third toss.

Answer :

If h and t represents heads and tails respectively, then when a coin is tossed three times, the sample space becomes


S = {(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT)},n(S)=8


Let E be the event of head occurring on the third toss, then the favorable outcomes will be


E = {(HHH, HTH, THH, TTH)}, n(E) = 4


So the corresponding probability will be



Let F be the event that head occurs on first two toss, then the favorable outcomes will be


F = {(HHH,HHT)}, n(F) = 2


So the corresponding probability will be



And the favorable outcome for getting head on all the three toss will be


(EF)={(HHH)}, n(EF)=1


And the corresponding probability becomes



So if head occurs on first two tosses, the probability of getting head on third tosses



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