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 ?

  1. A.

    7/8

  2. B.

    1/2

  3. C.

    7/16

  4. 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.

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