Question

A bag contains 1 blue, 2 white, and 2 red marbles. Match the columns. Drag the letter after a compound event in the left column and drop it before the matching probability in the right column. Select Submit to see if you are correct.

P(red and red), with replacement
P(white and white), without replacement
P(blue and red), with replacement
P(white and red), without replacement

A) 20%
B) 16%
C) 8%
D) 10%

Answer 1

What is the probability that you draw a red marble on your first try?

Answer 2

16%?

Answer 3

no that would to get both red marbles

Answer 4

That's correct! How did you figure it out?

Answer 5

well theres 2/5 x 2/5 = 4/25 and 4/25 is 16%

Answer 6

but what does with and without replacements mean?

Answer 7

For example, for P(red and red), with replacement: Replacement means that when you draw for the first time, you put the ball again in the bag. Without replacement means that after drawing a ball, you throw it away.

Answer 8

okay so the chance of getting 2 white marbles is 16% but two red marbles is a higher percent because its with replacements?

Answer 9

So for the second one, P(white and white) without replacement: For the first time, there are 5 balls in the bag. So P(white) is 2/5. But when you draw the first ball, you throw it away. So now there are 4 balls in the bag, one of them is white. So P(white and white) without replacement would be 2/5 * 1/4

Answer 10

so its 2/20 and 2/20 as a percent is 10% percent.

Answer 11

Right! Can you figure out the other two?

Answer 12

and one blue marble and 1 red marble is 8% correct?

Answer 13

Yes! Nice!

Answer 14

Could you explain the last one? [P(white and red), without replacement]

Answer 15

wait so its without replacements so it would be what you get on the first try correct?

Answer 16

You throw away what you get on the first try, instead of putting it again in the bag. What's the probability of getting a white ball on the first try?

Answer 17

oh the first try it would be 2/5

Answer 18

Good job! Now you throw away the white ball you got. What's the probability of getting a red on the second try?

Answer 19

the you would throw it away so now it would be 1/4?

Answer 20

Then*

Answer 21

Now you want a red, not a white one

Answer 22

and it would be the same thing correct? because there are 2 red marbles the chance that you get a red marble is 2/5 then you throw that away so now its 1/4, correct?

Answer 23

At your first try, you want a white one. There are 2 white marbles in 5, so the chance is 2/5. Given now that you got a white one on your first try, you throw it away. So there are 1 blue, 1 white and 2 red marbles left in the bag. You are now looking for a RED marble. There are 2 red marbles in the bag, and 4 marbles in total. So the chance you get a red one would be 2/4.

Answer 24

okay wait im confused without replacements means you throw one out.

Answer 25

yes

Answer 26

okay, so now that we got ride of a white one, would you use the original number "2/5" or would you use 1/4 now?

Answer 27

I will show you the steps graphically

http://www.sketchtoy.com/39028893

Answer 28

That is the first step. Drawing a white one. Remember that we are looking for P(white and red), without replacement

Answer 29

okay so then you would throw that out so now the chance of getting it is 1/4

Answer 30

Yes, but on the second try you are NOT looking for a white one again. You are looking for a red and there are 2 reds in 4 marbles. Let me draw it.

Answer 31

http://www.sketchtoy.com/39030148

Answer 32

okay so the chance of getting a red one is 2/4 do we want to throw that one out too?

Answer 33

You would if you were to pick another one. But you don't care now that the problem says P(white and red) without replacement. You have picked the 2 marbles, you're OK.

Answer 34

okay so the chance of getting a white marble was 2/5 then we threw it out so its now 1/4 and the chance of getting a red one is 2/4 so... 1/4 x 2/4 = .5, is this correct?

Answer 35

For the 1st try (white) it was 2/5. For the 2nd pick (red) it was 2/4. So 2/5 * 2/4 = 4/20 = 2/10 = 20%

Answer 36

ohh okay i understand now!

Answer 37

Thank you so much! i cant tell you how much this helped me!

Answer 38

I'm glad that I've helped!