Answer to Question #335891 in Statistics and Probability for Boh

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.

Question 11

What is the maximum value of 𝑐?

Question 12

What is 𝑃(𝐴|𝐵)?

Answer 1

Events A and B are mutually exclusive events,

$P(A) +P(B) \le1, \\ 0.37+c\le1,\\ c\le1-0.37,\\ c\le0.63.$

The maximum value of c is 0.63.

$P(A|B) =\cfrac{P(A\cap B) } {P(B) } =\cfrac{0 } {P(B) }=0.$

Mutually exclusive events can't happen simultaneously, so the probability of (A and B) is equal to zero.