Question

Events A and B are independent. Find the missing probability. Enter your answer as a decimal rounded to two places.

P(A)= 2/5, P( A and B) = 3/10, P(not B)= ?

Answer 1

ANSWER

$P(not \: B) = \frac{1}{4}$

EXPLANATION

If A and B are independent events, then

P(A and B)=P(A)×P(B)

$\frac{3}{10} = \frac{2}{5} \times \: P(B)$

Multiply both sides by;

$\frac{5}{2}$

$\frac{5}{2} \times \frac{3}{10} = \frac{5}{2} \times \frac{2}{5} \times \: P(B)$

$\frac{3}{4} =P(B)$

$P(not \: B) = 1 - P(B)$

$P(not \: B) = 1 - \frac{3}{4}$

$P(not \: B) = \frac{1}{4}$