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Consider a random experiment where two fair coins are tossed. Let A be the event that denotes HEAD on both the throws, B be the event that denotes HEAD on the first throw, and C be the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?

1. A and B are independent.
2. A and C are independent.
3. B and C are independent.
4. Prob(B|C) = Prob(B)

Correct answer: Prob(B|C) = Prob(B)

Solution

The statement Prob(B|C) = Prob(B) is true because the outcome of the first coin toss (event B) does not depend on the outcome of the second coin toss (event C). Since both coins are fair and independent, knowing the result of one does not affect the probability of the other.

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