Question

A bowl contains 4 yellow marbles and 3 red marbles. Eric randomly draws 3 marbles from the bowl. He replaces each marble after it is drawn. What is the probability that he draws 1 yellow marble and 2 red marbles?

Answer 1

Welcome to OpenStudy!

Answer 2

How many marbles are there in total in the bowl?

Answer 3

7

Answer 4

Right. When Eric draws the first marble, what's the probability that it will be yellow?

Answer 5

Hello?

Answer 6

4/7?

Answer 7

Correct. Very good. Now Eric puts the marble back in the bowl so there's still 4 yellow and 3 red marbles in the bowl. So it's just like we're back at the beginning again. Now, Eric draws another marble. What is the probability it will be red?

Answer 8

Hello?

Answer 9

3/7

Answer 10

Very good. Now Eric puts that marble back in the bowl and it's just like we're back at the beginning. Eric draws for the third time. What's the probability it will be red?

Answer 11

3/7

Answer 12

Good. In probability, these events are called independent events because one draw has no effect on the next one (Eric puts the marble back in the bowl). The total probability of drawing 1 yellow and 2 red is the product of the three individual probabilities, i.e.\[P = \frac{ 4 }{ 7 } \times \frac{ 3 }{ 7 } \times \frac{ 3 }{ 7 }\]What do you get?

Answer 13

36/343