Question

A bag contains 3 blue marbles, 9 green marbles, and 11 yellow marbles. Twice you draw a marble and replace it. Find P (blue, then green).

Answer 1

P(green and blue =
`(27)/(529)`

Explanation:

1) By the fundamental counting principle you can set up an expression to represent the problem:

*P(n) stands for probability of n

P(blue and green) = P(blue) x P(green)

2) Now figure out the values that should be substituted into the equation to find your desired probability.

3) First, Probability of green P(green):

Probability is defined as
`(succeeded \\\\\ outcomes)/(total \\ outcomes)`.

The succeeded outcomes are the ones you are looking for, in this case the probability that a green marble will be drawn. The total outcomes represents all of the possibilities, in this case, the total amount of marbles.

Thus P(green) =
`(9)/(23)`

4) Now find the probability of the blue P(blue) using the same method in step 3:

*One thing to note is that since the marbles are being placed back, the total succeeded outcomes/ total outcomes would not be changed at all. If the marbles were not replaced, then the values for total outcomes would be different and the values for succeeded outcomes may be different depending on what you're looking for.

P(Blue) =
`(3)/(23)`

5) Finally, insert these values into the above equation:

P(green and blue) =
`(9)/(23)  *(3)/(23)`

P(green and blue =
`(27)/(529)`