A bag contains 3 red and 5 black balls and second bag contains 6 red and 4 black balls. A ball is drawn from each bag. Find the probability that one is red and the other is black.

Explanation

Given:

`:'` Probability of getting a red ball from bag 1`=frac{3}{8}`.

`:'` Probability of getting a black ball from bag 1`=frac{5}{8}`.

`:'` Probability of getting a red ball from bag 2`=frac{6}{10}.`

`:'` Probability of getting a black ball from bag 2`=frac{4}{10}.`

`therefore` Probability of getting a red ball from bag 1 and black ball from bag 2`=frac{3}{8} cdot frac{4}{10}= frac{12}{80}=frac{3}{20} .`

`therefore` Probability of getting a black ball from bag 1 and red ball from bag 2`=frac{5}{8} cdot frac{6}{10}= frac{30}{80}=frac{3}{8}`

Therefore, the required probability is `=frac{3}{20}+frac{3}{8}`

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