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  • If A and B are mutually exclusive events, probability of event A equal to 0.35 and probability of event B equal to 0.45, find a probability of event A prime b probability of event B Prime c probability that of events A or B

If A and B are mutually exclusive events, P (A) = 0.35 and P (B) = 0.45, find
(a) P (A′)
(b) P (B′)
(c) P (A ∪ B)
(d) P (A ∩ B)
(e) P (A ∩ B′)
(f) P (A′∩ B′)

Answers (1)

P(A) = 0.35 & P(B) = 0.45     ….. (given)

P(A ∩ B) = 0        ……. (since A & B are mutually exclusive)

  1. P(A’)

Now, we know that,

P (A) + P (A’) = 1

0.35 + P (A’) = 1     

P(A’) = 1 – 0.35

P (A’) = 0.65

  1. P (B’)

Now, we know that,

P (B) + P (B’) = 1

0.45 + P (B’) = 1

P (B’) = 1 – 0.45

P (B’) = 0.55

  1. P (a u b)

Now, we know that,

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

P (A U B) = 0.35 + 0.45 – 0

P (A U B) = 0.80

  1. P (A ∩ B)

Since A & B are mutually exclusive events,

Thus, P (A ∩ B) = 0

  1. P (A ∩ B’)

P (A ∩ B’) = P (A) - P (A ∩ B)

= 0.35 – 0

= 0.35

  1. P (A’ ∩ B’)

P (A’ ∩ B’) = P (A U B)’

                  = 1 – P (A U B)

                  = 1 – 0.8    …… [from (c)]

                  = 0.2

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