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

Question

Philoid · Accepted 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

(E∩F)={(HHH)}, n(E∩F)=1

And the corresponding probability becomes

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