GATE Overflow Test Series | Probability | Test 1 | Question: 22

Question

Die A has three red and three green faces, whereas die B has four red and two green faces. A fair coin is flipped once. If it falls head, die A is chosen and if it falls tail die B is chosen. The chosen die is thrown repeatedly. If the first $4$ throws turn out to be red, what's the probability that die A is being used?

Answer 1

$P(A|rrrr) = \dfrac{P(A \cap rrrr)}{P(rrrr)}$

$\qquad = \dfrac{0.5 \times 0.5^4}{0.5 \times 0.5^4+0.5 \times 0.6667^4}=0.24$

Answer 2

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