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Let P[A] = P[B] = 1/3 and P[A ∩ B] = 1/10. Find the following: (a)...

Let P[A] = P[B] = 1/3 and P[A ∩ B] = 1/10.

Find the following:

(a) P[A ∪ Bc ]

(b) P[Ac ∩ B]

(c) P[Ac ∪ Bc ]

Now, let P[A] = 0.38 and P[A ∪ B] = 0.84.

(d) For what value of P[B] are A and B mutually exclusive?

(e) For what value of P[B] are A and B independent?

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