Supposed that A, B, and C are mutually independent events and that P(A)=0.5, P(B)=0.8, and P(C)=0.9. Find the probabilities that exactly two of the three events occur. Solution As they are mutually independent, P(ABC) = P(A) P(B) P(C) P(only 2 events to occur) = P(AB)- P(ABC) + P(B C)- P(ABC) +P(C A)- P(ABC) = 0.5*0.8 + 0.8*0.9 +0.9*0.5 - 3(0.5*0.8*0.9) = 0.49.

1. Supposed that A, B, and C are mutually independent events and that P(A)=0.5, P(B)=0.8, and
P(C)=0.9. Find the probabilities that exactly two of the three events occur.
Solution
As they are mutually independent, P(ABC) = P(A) P(B) P(C)
P(only 2 events to occur) = P(AB)- P(ABC) + P(B C)- P(ABC) +P(C A)- P(ABC) = 0.5*0.8 +
0.8*0.9 +0.9*0.5 - 3(0.5*0.8*0.9) = 0.49