Hello, Froggy. Let's begin.

1) You have confused something. If you need to find the probability that BOTH events A and B happen, you need to find P(A n B). If A and B are independent then P(A n B)=P(A)*P(B). You have already find it. It is equal to .3 * . 25 = .075. So the number of students are both taking honors courses and prefer basketball to football is .075*6000=450

2) We need to find P(A u B). So it is here where we use the formula P(A u B) = P(A) + P(B) - P(A n B).

a) If A and B are independent then P(A n B)=P(A)*P(B)=1/4*1/7=1/28. Then

P(A u B) = P(A) + P(B) - P(A n B)=1/4+1/7-1/28=10/28=5/14

b) If B is a subset of A then P(A n B)=P(B). Then

P(A u B) = P(A) + P(B) - P(B)=P(A)=1/4

3) The events A and B are called independent if P(A n B)=P(A)*P(B). So B is correct.

Hope this will help you. And one recommendation: learn your textbook more attentively. Good luck.

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