Suppose there are two coins. The first coin gives heads with probability 3/5 when tossed, while the second coin gives he...

Question

Suppose there are two coins. The first coin gives heads with probability 3/5 when tossed, while the second coin gives heads with probability 1/2. One of the two coins is picked up at random with equal probability and tossed. What is the probability of obtaining heads?

A. 1/2
B. 11/20
C. 7/10
D. 14/20

Accepted Answer

P(H) = 3/10 + 1/4 = 11/20. Answer key: C (11/20). This is a total probability problem. We pick coin 1 (probability 1/2) which gives heads with probability 3/5, or pick coin 2 (probability 1/2) which gives heads with probability 1/2. By the law of total probability: P(H) = (1/2)(3/5) + (1/2)(1/2) = 3/10 + 1/4. Let us compute: 3/10 + 1/4 = 6/20 + 5/20 = 11/20. Wait, let me recheck the options against the answer key C.