COMEDK 2024 Shift 2 Paper

To solve this problem, let's define the events clearly and use conditional probabilities.
Let: square
A be the event that the coin is tossed thrice, and
B be the event that a head does not appear on the first toss.
We need to find P(A∣B), the probability that the coin is tossed thrice given that a head does not appear on the first toss. Using Bayes' theorem, we have:

P(A∣B)=‌

P(A∩B)

P(B)

First, we calculate P(B), which is the probability that a head does not appear on the first toss. A fair coin has a 50% chance of landing heads or tails. Thus:
P(B)=‌

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Next, we consider the event A∩B, which is the event that the coin is tossed thrice, and a head does not appear on the first toss. For the coin to be tossed thrice, it must show tails on the first two tosses (because if it shows a head on the second toss, the experiment stops). The probability of getting tails on each toss is ‌

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, so:
Now, using these probabilities in Bayes' theorem:
Hence, the probability that the coin is tossed thrice given that a head does not appear on the first toss is:
Option A: ‌

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