Q. 285.0( 3 Votes )

Suppose a girl th

Answer :

Let,


be the event such that the girl gets 5 or 6 and hence tosses a coin 3 times


be the event such that the girl gets 1, 2, 3 or 4 and hence tosses a coin once.


A denotes the event such that the girl gets exactly one head.


P(E1) = P (5 or 6)


P(E1) = P(5) + P (6) =


P(E2) = P (1,2,3 or 4)


P(E2) = P(1) + P(2) +P(3) + P(4)


P(E2) =


A|E1 indicates that the probability of getting head if the girl gets 5 or 6 in dice and tosses a coin three times.


P = {Sample Space = HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}


Similarly,


P = 0.5 {Sample Space = {H,T}}


We need to find the probability of event that dice showed 1,2,3 or 4 if she got exactly one head that is we need to find P(E2|A).


This indicates that we need to use Baye’s theorem-


From Baye’s Theorem:


P(E2|A) =


P(E2|A) =


The required probability is


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