Question

There are 8 red marbles, 2 green marbles, and 5 blue marbles in a bag. Marbles are replaced after each draw. What is the probability that the first marble drawn is red and the second marble drawn is green?

Answer 1

`(16)/(225)`

Explanation:

When attempting probability problems we want to figure out the chances of something happening. This turns into something like:

`\frac{\text{marble drawn}}{\text{total marbles}}`

In this case we have 8 red marbles, 2 green marbles, and 5 blue marbles in a bag. That brings us to a total of 15 marble.

Since we want to first draw a red marble the chance of that happening would be:

`\frac{8\text{(the marble drawn)}}{15\text{(total # of marbles)}}`
Now we replace the marble as stated in the problem so we then draw the next marble, which is green.

`\frac{2\text{(the marble drawn)}}{15\text{(total number of marbles)}}`

All that's left is to multipy the values we got:

`(8)/(15) *(2)/(15)=(16)/(225)`

That's our answer.