A basket contains 5 apples and 7 oranges,and | vedclass

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(D) Let $B_1$ be the first basket and $B_2$ be the second basket.Total fruits in $B_1 = 5 + 7 = 12$.Total fruits in $B_2 = 4 + 8 = 12$.Probability of

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$\frac{76}{144}$

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(D) Let $B_1$ be the first basket and $B_2$ be the second basket.Total fruits in $B_1 = 5 + 7 = 12$.Total fruits in $B_2 = 4 + 8 = 12$.Probability of picking an apple from $B_1 = \frac{5}{12}$.Probability of picking an apple from $B_2 = \frac{4}{12}$.Probability of picking an orange from $B_1 = \frac{7}{12}$.Probability of picking an orange from $B_2 = \frac{8}{12}$.Since the events are independent,the probability that both are apples is $\frac{5}{12} 	imes \frac{4}{12} = \frac{20}{144}$.The probability that both are oranges is $\frac{7}{12} 	imes \frac{8}{12} = \frac{56}{144}$.Since these events are mutually exclusive,the total probability is $\frac{20}{144} + \frac{56}{144} = \frac{76}{144}$.

$A$ basket contains $5$ apples and $7$ oranges,and another basket contains $4$ apples and $8$ oranges. One fruit is picked out from each basket. Find the probability that the fruits are both apples or both oranges.

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