Question

Kendra has a bowl containing 10 blue marbles, 15 yellow marbles, 5 green marbles, and red marbles of the same size. She will randomly put out a marble, keep it outside the bowl, then pull out another marble.

What is the probability she will draw a red marble and then a yellow marble?

1/14
5/72
1/18
3/20

Answer 1

The answer is 1/14.

There are in total 36 marbles:
10 blue + 15 yellow + 5 green + 6 red.

The probability to put out a red marble in the first draw is 6 out of 36 marbles because there are 6 red marbles of total 36:
P(r) = 6/36 = 1/6.

After that 1 red marble is outside the bowl, there are now 35 marbles in total.
The probability to put out a yellow marble in the second draw is 15 out of 35 because there are 15 yellow marbles of total 35 marbles:
P(y) = 15/35 = 3/7.

If we want both these events to occur (1. to draw the red marble and 2. to draw the yellow marble), we will use a multiplication rule. The multiplication rule calculates the probability that both of two events will occur:
P(r) × P(y) = 1/6 × 3/7 = 3/42 = 1/14.

Therefore, the probability Kendra will draw a red marble and then a yellow marble is 1/14.