Vishnu has two jars of marbles, Jar A and Jar B. Jar A contains 3 yellow marbles and 2 green marbles. Jar B contains 4 yellow marbles and 3 green marbles. Vishnu flips a fair coin. If it lands heads, he picks two marbles at random without replacement from Jar A. If it lands tails, he picks two marbles at random with replacement from Jar B. Given that Vishnu picked one yellow and one green marble, what is the probabil

Step-by-step solution

Let E₁ be the event of choosing Jar A and E₂ be the event of choosing Jar B. P(E₁) = 1 2 , P(E₂) = 1 2 Let E be the event of drawing one yellow and one green marble. For Jar A (without replacement): P(E|E₁) = ³C₁ ²C₁ ⁵C₂ = 3 2 10 = 3 5 For Jar B (with replacement): P(E|E₂) = 4 7 3 7 + 3 7 4 7 = 24 49 Using Bayes' theorem, the required probability is: P(E₂|E) = P(E₂)P(E|E₂) P(E₁)P(E|E₁) + P(E₂)P(E|E₂) P(E₂|E) = 1 2 24 49 1 2 3 5 + 1 2 24 49 P(E₂|E) = 24 49 3 5 + 24 49 = 24 49 147 + 120 245 P(E₂|E) = 24 49 245 267 =