A coin is tossed three times. Find P (A/B) in each of the following:

A=Heads on third toss, B=Heads on first two tosses

When a coin is tossed three times, we have following outcomes

{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Total outcomes =8

From above outcomes,

A= Heads on third toss = {HHH, HTH, THH, TTH} =4

Therefore probability of occurrence of event A = P(A) =

B= heads on first two tosses = {HHH, HHT} =2

Therefore probability of occurrence of event B = P(B) =

Also we want P (A ∩ B) = probability of occurrence of both events A and B

=heads on first two tosses and heads on third toss

=heads on all tosses = {HHH} = 1(Occurrence Of both A and B events

Therefore, P (A ∩ B) =

Hence, =

==(answer)