Thread: Probability Problem

One jar contains 6 blue marbles, 5 red marbles, 8 white marbles, and 8 goldenrod marbles. A second jar contains 8 blue marbles, 7 red marbles, 8 white marbles, and 6 goldenrod marbles. A marble is picked at random from the first jar and put into the second jar. A marble is then selected at random from the second jar. Find the probability that the marble selected from the second jar is a goldenrod. Give answer as a fraction reduced to lowest terms.

I think this problem is easier than I think but I keep getting messed up. Help please!

I will do

Hello, sweeetcaroline!

I'll simplify the wording . . .

One jar contains 8 Gold marbles and 19 Others.
A second jar contains 6 Gold marbles and 23 Others.
A marble is picked at random from the first jar and put into the second jar.
A marble is then selected at random from the second jar.
Find the probability that the marble selected from the second jar is Gold.

There are two cases to consider . . .


[1] The first marble drawn is Gold: .
. . .Then the second jar contains: 7 Gold and 23 Others: .
. . .


[2] The first marble drawn is an Other: .

. . .Then the second jar contains: 6 Gold and 24 Others: .

. . .


Therefore: .