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A box B1 contains 1 white ball and 3 red balls. Another box B2 contains 2 white balls and 3 red balls. If one ball is drawn at random from each of the boxes B1 and B2, then find the probability that the two balls drawn are of the same colour. |
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Answer» \(P\left(\frac{W}{B_1}\right) = \frac14\) \(P\left(\frac{R}{B_1}\right) = \frac34\) \(P\left(\frac{W}{B_2}\right) = \frac25\) \(P\left(\frac{R}{B_2}\right) = \frac35\) Probability that both drawn ball from boxes B1 & B2 are of same colour \(= P\left(\frac{W}{B_1}\right) P\left(\frac{W}{B_2}\right) + P\left(\frac{R}{B_1}\right) P\left(\frac{R}{B_2}\right)\) \(= \frac 14 \times \frac 25 + \frac 34 \times \frac 35\) \(= \frac2 {20 } + \frac 5 {20}\) \(= \frac{11}{20}\) |
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