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.$B_1$ contains $5$ apples and $7$ oranges (Total = $12$ fruits).$B_2$ contains $4$ ap

Vedclass · Accepted Answer

$\frac{76}{144}$

Vedclass · Answer

(D) Let $B_1$ be the first basket and $B_2$ be the second basket.$B_1$ contains $5$ apples and $7$ oranges (Total = $12$ fruits).$B_2$ contains $4$ apples and $8$ oranges (Total = $12$ fruits).Probability of picking an apple from $B_1$ is $P(A_1) = \frac{5}{12}$.Probability of picking an orange from $B_1$ is $P(O_1) = \frac{7}{12}$.Probability of picking an apple from $B_2$ is $P(A_2) = \frac{4}{12}$.Probability of picking an orange from $B_2$ is $P(O_2) = \frac{8}{12}$.The probability that both are apples is $P(A_1 \cap A_2) = \frac{5}{12} 	imes \frac{4}{12} = \frac{20}{144}$.The probability that both are oranges is $P(O_1 \cap O_2) = \frac{7}{12} 	imes \frac{8}{12} = \frac{56}{144}$.The total probability is $P = \frac{20}{144} + \frac{56}{144} = \frac{76}{144}$.

$A$ 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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