Question

suppose you choose a marble from a bag containing 4 red marbles, 2 white marbles, and 3 blue marbles. You return the first marble to the bag and then choose again. Find the P(red and blue).

Answer 1

would it be 7/9

Answer 2

There are two rules:

The AND rule

The OR rule

Answer 3

In the AND rule you multiply but in the OR rule you add

Answer 4

But since its saying P(red and blue) that means you will multiply not add

Answer 5

ok so you add 4 times 2 times 3?

Answer 6

These are independent events because you are doing this "with replacement". So, you would take the first probability multiplied by the second probability multiplied by 2 because you could have red and then blue or blue and then red. Start with P(red) for just one pick, can you determine that first?

Answer 7

No, your answer will be P(red) x P(blue) x 2. Let's work on P(red) first. Nine marbles in all of which 4 are red. So, P(red) = (# red)/(total # of marbles)

Answer 8

P(blue) is similar to P(red) but with different numbers. 3 blue marbles, but still 9 total marbles in all. How are you coming along with P(red)?

Answer 9

so P(red)=(4)/(24)

Answer 10

so P(red)= (4)/(9)

Answer 11

Yes! Now do P(blue).

Answer 12

P(Blue)=(3)/(9)

Answer 13

Good! Now, as stated above P(red and blue) = P(red) x P(blue) x 2 because the problem reads like it allows for either red or blue to be picked first. That's why there is a factor of "2" added on.

Answer 14

ok Im with you im just a little confused

Answer 15

(4)/(9)*(3)/(9)* 2

Answer 16

np. Once we have this overall view, we need to drill down into understanding. The whole key to this problem begins with "replacing", so we always have 9 total marbles, we also have independence (which tells us to multiply the probabilities), and we have a factor of "2" because the order doesn't matter. Ask questions now. Just saw your answer and it's right! Good job!

Answer 17

ok so what would the answer be then because i have to change it to fraction form

Answer 18

it would be 36*27*2?

Answer 19

\[\frac{ 4 }{ 9 }\times \frac{ 3 }{ 9 }\times2 = \frac{ 8 }{ 27 }\]

Answer 20

but 8/27 is not on my answer thing

Answer 21

Then the problem is written poorly. You probably have 4/27 on your answer guide, right?

Answer 22

yes

Answer 23

The problem is definitely written poorly and you should tell your teacher, because they left out red FIRST and then blue. That is what they intended, but they didn't say or imply that.

Answer 24

nope but thanks for helping me

Answer 25

The way the problem reads, it could be the case that blue gets picked first and then red and then you would still have red and blue. Bad problem.

Answer 26

yea i know

Answer 27

I have a brother who has a doctorate in education, and he knows nothing about math. And it's people like him who design a lot of these questions!

Answer 28

ha Probably :) can you help on my next one

Answer 29

Sure, why not?