Probability Question

Question

Couldn’t figure out this problem for the life of me!

There are 16 marbles in a bag. 6 blue marbles, 7 red marbles, and 3 free marbles. What is the probability that if 3 marbles are selected without replacement that I choose one of each.

Thanks guys,

have a wonderful day and stay happy :)

Answer 1

I'm not sure what "free" marbles are but, maybe you made a typo, I'll just assume "free" is a color.

Let's assume we are going to pick blue, red, and free in that order

Pick #1: The probability of drawing a blue is 6/16 or 3/8

Pick #2: The probability of drawing a red is 7/15 (since you already picked one marble out and didn't replace it)

Pick #3: The probability of drawing a free is 3/14

Then the probability of all 3 of those things happening is 3/8 x 7/15 x 3/14 = 63/1680 = 3/80

Let's say instead, you pick the red, blue, and free. Then:

Pick #1: 7/16

Pick #2: 6/15

Pick #3: 3/14

Total Probability = 7/16 x 6/15 x 3/14 = 126/3360 = 3/80

You can try the other possible orders, but it won't matter, the probability of getting one of each color will be 3/80