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

a.

$$Red=\{1,2,3,4,5\}$$

$$Blue=\{1,2,3,4,5,6,7,8\}$$

$$P(even|red)=\dfrac{2}{5}$$

b.

$$Red=\{1,2,3,4,5\}$$

$$Blue=\{1,2,3,4,5,6,7,8\}$$

$$P(red|even)=\dfrac{2}{6}=\dfrac{1}{3}$$