Suppose A and B are event such that PA 04 and PA U B 06 fi

Suppose A and B are event such that P(A) = 0.4 and P(A U B) = 0.6, find the probability of the B\' the complemnt of B if

a) the events A and B mutually excusive.

b) the events A and B are independent.

Solution

a)

If A and B are mutually exclusive,

P(A U B) = P(A) + P(B)

Thus,

0.6 = 0.4 + P(B)

P(B) = 0.2

Thus,

P(B\') = 1 - P(B) = 0.8 [answer]

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b)

If they are independent,

P(A n B) = P(A) P(B)

As

P(A U B) = P(A) + P(B) - P(A n B)

Then

0.6 = 0.4 + P(B) - P(A)P(B)

0.2 = P(B)[1 - P(A)]

0.2 = P(B)[1 - 0.4]

P(B) = 0.3333333333

Thus,

P(B\') = 1 - P(B) = 0.666666667 [answer]