Let event A: Fair coin is tossed,
event B: Fake coin is tossed
and event H: Head occur.
Clearly, a fair coin has one head.
∴ Probability that head occur under the condition that the fair coin is tossed = P(H/A) = 1/2
Fake coin has two heads.
∴ Probability that head occur under the condition that the fake coin is tossed = P(H/B) = 1
n(A) = 2, n(B) = 1, n(S) = 3
∴ P(A) = \(\frac {n(A)}{n(S)} = \frac {2}{3}\)
∴ P(B) = \(\frac {n(B)}{n(S)} = \frac {1}{3}\)
(i) Required probability P(H) = P(A) P(H/A) + P(B) P(H/B)
(ii) Required probability = P(B/H)
By Baye’s theorem
= 1/2.