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Mathematics · JEE | PROBABILITY
हिन्दीSuppose a girl throws a die. If she gets 5 or 6, she tosses a coin three times and notes heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4?
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Correct answer · Option D
\( \frac{8}{11} \)
Explanation
Let \( E_1 \) be getting 1,2,3,4 (prob \( \frac{2}{3} \)) and \( E_2 \) be getting 5,6 (prob \( \frac{1}{3} \)). \( P(A|E_1) = \frac{1}{2} \), \( P(A|E_2) = 3(\frac{1}{2})^3 = \frac{3}{8} \). By Bayes' theorem, \( P(E_1|A) = \frac{\frac{2}{3}(\frac{1}{2})}{\frac{2}{3}(\frac{1}{2}) + \frac{1}{3}(\frac{3}{8})} = \frac{1/3}{1/3 + 1/8} = \frac{8}{11} \).
