Question

Check my work PLEASE
Probability Math Help Please
1. A container holds 12 red marbles, 10 blue marbles, and 14 green marbles. You will randomly select two marbles without replacement.
(a) Fill in the probabilities on each branch of the tree diagram. Use the boxes with the fraction bars already provided.
(b) Use the tree diagram to answer the following:
How many ways can you select the marbles?
How many ways can you select exactly 1 blue marble?
What is the probability that you select 2 red marbles?
What is the probability that you select a green marble and then a red marble?

Answer 1

b1
There are 9 ways to select the marbles
correct?

Answer 2

b2
there are 5 ways to select 1 blue marble
yes?

Answer 3

b3
12/36 * 11/35 = 132/1260
correct?

Answer 4

b4
14/36 * 11/35 = 154/1260
yes?

Answer 5

The tree looks good in part (a)

Answer 6

`b1`
`There are 9 ways to select the marbles`
`correct?`

yes that is correct. There are 3*3 = 9 ways to pick 2 marbles. As you can see, there are 9 branches on the tree

Answer 7

`b2`
`there are 5 ways to select 1 blue marble`
`yes?`

Incorrect. Look through the tree. Count the number of times blue comes up once. If you want, you can list out the sample space

RR
RB
RG

BR
BB
BG

GR
GB
GG

where B = blue, R = red, G = green

How many times does blue come up exactly once? Be careful. BB has blue come up twice so that doesn't count.

Answer 8

`b3`
`12/36 * 11/35 = 132/1260`
`correct?`

Correct, but don't forget to reduce any fractions as much as possible. You can reduce 132/1260 further.

Answer 9

`b4`
`14/36 * 11/35 = 154/1260`
`yes?`

Incorrect. See attached for a hint

Answer 10

so on b2
since BB doesn't count because it has 2 blues the answer is then you have 4 possibilities of selecting a blue marble

Answer 11

b4
14/36 * 12/35 = 168/1260

Answer 12

`so on b2`
`since BB doesn't count because it has 2 blues the answer is then you have 4 possibilities of selecting a blue marble`

that is correct. The four cases where blue (B) comes up exactly once are

RB
BR
BG
GB

Answer 13

`b4`
`14/36 * 12/35 = 168/1260`

better but don't forget to reduce

Answer 14

Thank you so much!!!

Answer 15

no problem