A bag contains three coins two of the coins are fake one has

A bag contains three coins: two of the coins are fake: one has heads on each side, and the other has tails on both sides. The third coin is normal. Each coin is fair (if you flip it, the probability either side coming up is 0.5). A coin is selected randomly from the bag and flipped.

(a) What is the probability that a head appears?

(b) If a head appears, what is the probability that the other side of the coin is also heads?

Solution

the probability of selecting any coin out of three= 1/3

1)probablility that a head appears= 1/3*1/2 + 1/3*1 +1/3*0 = 3/6= 1/2

2) use bayes theorem,conditional probability-

P(B/A) =P(B,A)/P(A)

where P(A)-probability that a head appears

P(B)- other side of coin is also heads

hence, P(B/A) = (1/2 )