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A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is 

  • a)
    1/8

  • b)
    3/4 

  • c)
    3/8

  • d)
    1/2

Correct answer is option 'D'. Can you explain this answer?
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Solution:

Given, a fair coin is tossed three times in succession.

Let us consider the events,

H: Getting a head on the first toss
T: Getting a tail on the first toss

Now, we need to find the probability of getting exactly two heads in three tosses given that the first toss produces a head.

Let us consider the following cases,

Case 1: HHT

The probability of getting HHT given that the first toss produces a head is (1/2) x (1/2) = 1/4.

Case 2: HTH

The probability of getting HTH given that the first toss produces a head is (1/2) x (1/2) = 1/4.

Case 3: HTT

The probability of getting HTT given that the first toss produces a head is (1/2) x (1/2) = 1/4.

Therefore, the probability of getting exactly two heads in three tosses given that the first toss produces a head is the sum of probabilities of the above three cases.

P(exactly two heads in three tosses | first toss produces a head) = 1/4 + 1/4 + 1/4 = 3/4.

Hence, the correct answer is option D, 3/4.
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