Question

A jar contains 5 red marbles numbered 1 to 5 and 8 blue marbles numbered 1 to 8 . A marble is drawn at random from the jar. Find the probability the marble is

a. Even-numbered given that the marble is red.

b. Red given that the marble is even-numbered.

Answer 1

$P(Red) = \frac{5}{13}$

$P(Blue)=\frac{8}{13}$

$P(Even)=\frac{6}{13}$

$P(odd)=\frac{7}{13}$

P(Even given Red) = $P(Even|Red)=\frac{2}{5}$

P(Red given Even) = $P(Red|Even)=\frac{2}{6}=\frac{1}{3}$

(a) $P(Even|Red)=\frac{P(Red|Even)×P(Even)}{P(Red)}$

$=>P(Even|Red)=\frac{\frac{2}{6}×\frac{6}{13}}{\frac{5}{13}}=\frac{2}{5}$

(b) $P(Red|Even)=\frac{P(Even|Red)×P(Red)}{P(Even)}$

$=>P(Red|Even)=\frac{\frac{2}{5}×\frac{5}{13}}{\frac{6}{13}}=\frac{1}{3}$