If A and B are two mutually exclusive events, and P(A) = 0.55, P(B) = 0.3, then find: P(A U 𝐵𝑐) & P(𝐴𝑐 ∩ B)

Question

If A and B are two mutually exclusive events, and P(A) = 0.55, P(B) = 0.3, then find:

a.  P(A U 𝐵^𝑐)

b.  P(𝐴^𝑐 ∩ B)

Answer 1

Given:

P(A) = 0.55

P(B) = 0.3

∴P(B^c) = 1-0.3 = 0.7

P(A^c) = 1-0.55= 0.45

Since A and B are disjoint (mutually exclusive)

∴A ⊆ B^c and B ⊆ A^c

∴ A ∪ B^c = B^c and B ∪ A^c = A^c

^

(a)P(A ∪ B^c) = P(B^c) =0.7

(b) P(A^c ∪ B) = P(A^c) = 0.45