Probability Question 427

Question: 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

[AMU 2002]

Options:

A) $ \frac{24}{144} $

B) $ \frac{56}{144} $

C) $ \frac{68}{144} $

D) $ \frac{76}{144} $

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Answer:

Correct Answer: D

Solution:

  • Required probability = $\frac{^{5}C_1 \cdot ^{4}C_1}{^{12}C_1 \cdot ^{12}C_1}+\frac{^{7}C_1 \cdot ^{8}C_1}{^{12}C_1 \cdot ^{12}C_1}$ $ =\frac{20+56}{144}=\frac{76}{144} $ .



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