Question

A bag contains 5 red marbles, 4 blue marbles, and 3 yellow marbles. A student removes 1 marble without looking and records the color. He then places the marble back in the bag before drawing another marble. What is the probability of drawing a color other than blue, then drawing a yellow marble?

A) 29/60
B) 19/60
C) 4/15
D) 11/30

Answer 1

The probability of drawing a color other than blue, then drawing a yellow marble is 1/6.

Step-by-step explanation:

To find the probability of drawing a color other than blue, then drawing a yellow marble, we need to determine the probabilities of each event separately and then multiply them together.

The probability of drawing a color other than blue on the first draw is equal to the number of marbles that are not blue (5 red + 3 yellow) divided by the total number of marbles (5 red + 4 blue + 3 yellow).

Probability of drawing a color other than blue = (5 + 3) / (5 + 4 + 3) = 8 / 12 = 2 / 3.

Since the marble is placed back in the bag before the second draw, the probability of drawing a yellow marble is equal to the number of yellow marbles (3 yellow) divided by the total number of marbles (5 red + 4 blue + 3 yellow).

Probability of drawing a yellow marble = 3 / 12 = 1 / 4.

To find the probability of drawing a color other than blue, then drawing a yellow marble, we multiply the probabilities of each event:

Probability of drawing color other than blue, then drawing yellow marble = (2 / 3) * (1 / 4) = 2 / 12 = 1 / 6.