Question:
Two biased coins \( C_1 \) and \( C_2 \) have probabilities of getting heads \( \frac{2}{3} \) and \( \frac{3}{4} \), respectively. When tossed. If both coins are tossed independently two times each, then the probability of getting exactly two heads out of these four tosses is
Two biased coins \( C_1 \) and \( C_2 \) have probabilities of getting heads \( \frac{2}{3} \) and \( \frac{3}{4} \), respectively. When tossed. If both coins are tossed independently two times each, then the probability of getting exactly two heads out of these four tosses is
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When solving probability problems involving multiple events, use the binomial distribution formula to calculate individual outcomes and combine them as needed.
Updated On: Dec 12, 2025
- \( \frac{1}{4} \)
- \( \frac{37}{144} \)
- \( \frac{41}{144} \)
- \( \frac{49}{144} \)
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The Correct Option is B
Solution and Explanation
Step 1: Analyzing the coin tosses.
For each coin, we calculate the individual probabilities of getting heads for exactly two tosses out of four using the binomial distribution formula. Step 2: Computing the total probability.
By calculating the individual outcomes and adding them together, we find the probability of getting exactly two heads. Step 3: Conclusion.
The correct answer is (B) \( \frac{37}{144} \).
For each coin, we calculate the individual probabilities of getting heads for exactly two tosses out of four using the binomial distribution formula. Step 2: Computing the total probability.
By calculating the individual outcomes and adding them together, we find the probability of getting exactly two heads. Step 3: Conclusion.
The correct answer is (B) \( \frac{37}{144} \).
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