Question

Assume a jar has 7 red marbles and 5 black marbles. Draw out 3 marbles with and without replacement. Find the requested probabilities.

(c) P(one red and two black marbles)
With replacement , without replacement .

(d) P(red on the first draw and black on the second draw and black on the third draw)
With replacement , without replacement .

Answer 1

What does with replacement mean?

Answer 2

putting back in the jar

Answer 3

Oh. I dunno about that, but without replacement is pretty easy.

Answer 4

i understand more of the with replacement but if you can help with the without replacement that would be good

Answer 5

For the first question of one red and two black we just want to know how many ways we can choose one red, and two black divided by how many ways we can choose 3 marbles from 12.

So:
\[\frac{{7 \choose 1} * {5 \choose 2}}{12 \choose 3}\]

Answer 6

so 12/3?

Answer 7

No,
7 choose 1 = 7
5 choose 2 = 10
12 choose 3 = 220
So it is 70/220.

Are you familiar with the choose function (and it's notation)?

Answer 8

kind of

Answer 9

was that without replacement?

Answer 10

Yes

Answer 11

do you know how to do d?

Answer 12

For the other one it's just

(Probability of choosing a red)*(Probability of choosing a black)*(Probability of choosing a black)

So (7/12) * (5*/11) * (4/10)

Answer 13

140/1320....can be reduced though right?

Answer 14

14/132 = 7/66