Question

Suppose A and B are mutually exclusive events defined on the same sample space such that P(A)=0.37 and P(B)=c.

1. What is the maximum value of c?

2. What is P(A|B)?

Answer 1

Solution:

(1):

For mutually exclusive, P(A)+P(B)=P(AUB) and P(A$\cap$B)=0

P(A)+P(B)=P(AUB)

$\Rightarrow$ 0.37+c=1 [Since P(AUB)$\le$ 1 and we need maximum value of c]

$\Rightarrow$c=0.63

(2):

$P(A|B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{0}{0.63}=0$