A and B are two events in the same sample space PA or B075 P

A and B are two events in the same sample space. P(A or B)=0.75. P(A)=0.5 and

P( A andB^c)= 0.35.

a) Find P(B).

b)

Find P( A and B)

B). Are A and B mutually exclusive?

Solution

a)

Note that

P(B) = P(A or B) - P(A and Bc)

= 0.75 - 0.35

= 0.40 [ANSWER]

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b)

P(A and B) = P(A) - P(A and Bc)

= 0.5 - 0.35

= 0.15 [ANSWER]

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c)

No, since P(A and B) is not equal to 0. [ANSWER]