Question

A box contains three coins: two fair coins and one fake two-headed coin. A coin is picked randomly from the box and tossed. 

(i) What is the probability that it lands head up? 

(ii) If happens to be head, what is the probability that it is the two-headed coin?

Answer 1

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.