Question

WILL MEDAL. Two marbles are to be pulled from a bag that contains 2 yellow marbles, 4 green marbles, and 6 orange marbles. After the first marble is drawn, it is not replaced What is the probability that both marbles will be the same color?

Answer 1

Bag: 2Y 4G 6O, draw two without replacement.
How many in all?

Answer 2

12 in all @mathmate

Answer 3

Good!
Have you learned about "combinations", such as \(C^4_2\)?

Answer 4

no

Answer 5

Can you name me the outcomes that could be considered "success"?

Answer 6

im not quite sure how to do this.

Answer 7

Is YY a success, or is YG a success?

Answer 8

yy?

Answer 9

Success is considered the events that are included in our calculation of probabilities.

Answer 10

Correct!
Can you name all events that are successes?

Answer 11

gg and oo?

Answer 12

Perfect.
Now you will have to calculate the probability of the three cases which lead to success, namely YY, GG and OO.
So far so good?

Answer 13

so would it be y * y and g*g or?

Answer 14

@mathmate

Answer 15

@sar12389 Say, what is the probability of getting a Y on the first draw?

Answer 16

2/12

Answer 17

4/12 g and 6/12 o @mathmate

Answer 18

Good, have you done the multiplication law?

Answer 19

im not sure

Answer 20

Good, all three are correct for the _first_ draw.
Now what is the probability of getting another Y after the first Y?

Answer 21

1/12?

Answer 22

3/12 g and 5/12 o

Answer 23

@mathmate

Answer 24

For YY, first one is 2/12, second is 1/11 (they do not replace).
So by the multiplication law, the probability of YY is (2/12)*(1/11)=2/132.
You can try the other two.
The answer is the sum of all three, P(YY)+P(GG)+P(OO).

Answer 25

so 43/132 ? what would the percent be @mathmate

Answer 26

i have to choose from 79.5%, 81.5% , 85% or 90%

Answer 27

i have to choose from 79.5%, 81.5% , 85% or 90%

Answer 28

You would do a division of 43/132.
For probability, I prefer to keep the fractions.
Note: I think I got a different number. Can you check?

Answer 29

i got 0.3257

Answer 30

@mathmate

Answer 31

That corresponds to 43/132.

As I said, 0.3257 is a (rounded) approximately number. 43/132 is exact, which is preferred in probabilities.

But I get a slightly different number than 43/132.

Answer 32

what is the percent? @mathmate

Answer 33

I get (2*1+4*3+6*5)/(12*11)=1/3=33% for two marbles of the same colour,
and (2*10+4*8+6*6)/(12*11)=2/3=67% for two marbles of different colours.
I do not know from where the choices came.
All I can suggest is to reread the question to make sure there are no typos.