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------------------------------------------------ A pesticide is used to control aphids. The number of aphids ($Y$) killed by the insecticide follows a binomial distribution with parameter $p = 0.75$.

What's the probability for the following scenarios?

(a) Exactly 5 out of 10 aphids are killed?
(b) More than 8 out of 12 aphids are killed?
(c) Less than 3 out of 8 aphids are killed?
(d) Exactly 7 out of 15 aphids are killed?

To solve these probabilities, we can use the binomial distribution formula. For (a) Exactly 5 out of 10 aphids being killed, we calculate P(X=5) = C(10, 5) * (0.75)^5 * (0.25)^5. For (b) More than 8 out of 12 aphids being killed, we calculate P(X > 8) = P(X=9) + P(X=10) + P(X=11) + P(X=12). For (c) Less than 3 out of 8 aphids being killed, we calculate P(X < 3) = P(X=0) + P(X=1) + P(X=2). And for (d) Exactly 7 out of 15 aphids being killed, we calculate P(X=7) = C(15, 7) * (0.75)^7 * (0.25)^8. Substitute the values and calculate to get the probabilities.

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