Suppose there are two coins. The first coin gives heads with probability 5/8…
2007
Suppose there are two coins. The first coin gives heads with probability 5/8 when tossed, while the second coin gives heads with probability 1/4. One of the two coins is picked up at random with equal probability and tossed. What is the probability of obtaining heads ?
- A.
7/8
- B.
1/2
- C.
7/16
- D.
5/32
Attempted by 15 students.
Show answer & explanation
Correct answer: C
Solution: Use the law of total probability because one of the two coins is chosen at random.
Probability of heads with the first coin = 5/8. Weight by the chance of picking that coin (1/2): 1/2 * 5/8 = 5/16.
Probability of heads with the second coin = 1/4. Weight by the chance of picking that coin (1/2): 1/2 * 1/4 = 1/8 = 2/16.
Add the weighted probabilities: 5/16 + 2/16 = 7/16.
Answer: 7/16.