Explanation

(d)
$P$ (selecting an apple from both baskets)
$= P$(apple from first basket) $\bullet P$(apple from second basket)
$= \frac{{\ ^{5}C}_{1}}{{\ ^{12}C}_{1}} \bullet \frac{{\ ^{4}C}_{1}}{{\ ^{12}C}_{1}}$
$P$ (selecting a orange from both baskets)
$= P$(orange from first basket) $\bullet P$(orange from second basket)
$= \frac{{\ ^{7}C}_{1}}{{\ ^{12}C}_{1}} \bullet \frac{{\ ^{8}C}_{1}}{{\ ^{12}C}_{1}}$
Required probability $= \frac{{\ ^{5}C}_{1}{\ ^{4}C}_{1}}{{\ ^{12}C}_{1}{\ ^{12}C}_{1}} + \frac{{\ ^{7}C}_{1}{\ ^{8}C}_{1}}{{\ ^{12}C}_{1}{\ ^{12}C}_{1}}$
$= \frac{20 + 56}{144} = \frac{76}{144}$