A bag A contains 4 black and 6 red balls and bag B contains 7 black and 3 red balls. A die is thrown. If 1 or 2 appears on it, then bag a is chosen, otherwise bag B. If two balls are drawn (without replacement) from the selected bag, find the probability of one of them being red and another black.

Explanation

Suppose `E_{1}=` choosing bag `A`, and `E_{2}=` choosing bag `B`

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therefore P(E_{1})=frac{1}{3}`



`P(E_{2})=frac{2}{3}`


`A=` one red and one black ball

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therefore P(A / E_{1})=frac{{ }^{4} C_{1} cdot{ }^{6} C_{1}}{{ }^{10} C_{2}}=frac{8}{15}`


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