Write the appropriate formula for Do not use spaces Use to

Write the appropriate formula for:

(Do not use spaces. Use * to represent multiplication, and the word NULL in capitol letters to represent null set. Write letter symbols in capitols e.g. P(A)).

(a) If the events A and B are mutually exclusive, then n(A B) =

(b) If the events A and B are mutually exclusive, then P(A B) =

(c) If the events A and B are independent, then P(A B) =

(d) If the events A and B are independent, then P(A|B)

Solution

When A, B are mutually exclusive P( A n B) = 0

A, B are independent P( A n B) = P(A) * P(B)

(a) If the events A and B are mutually exclusive, then n(A B) = 0

(b) If the events A and B are mutually exclusive, then P(A B) = P(A) + P(B)

(c) If the events A and B are independent, then P(A B) = P(A) * P(B)

(d) If the events A and B are independent, then P(A|B) = P( A n B) / P(B) = P(A) * P(B)/P(B) = P(A)