Question

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

(b) P(3 black marbles)
With replacement , without replacement .

(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

a) with replacement:
P(3 red) = P(1st red). P(2nd red). P(3rd red)=(7/10)(7/10)(7/10)=343/1000

Answer 2

these are the answers I got I just wanted to get them checked and see if they are right?
a) with 343/128 without 21/132
b)125/1728 without 60/132
c) I did not know how to do this one
D) with 175/1728 without 14/132

Answer 3

wouldnt it be 7/12? not 7/10?

Answer 4

Oh sorry over 12 :(

Answer 5

ok could you possibly tell me if my answers are right? and possibly how to do C?

Answer 6

for a with replacement: P(3 red)=(7/12)^3

Answer 7

without replacement: P(3 red)=(7/12)(6/11)(5/10)=....

Answer 8

Use the same method to solve B.

Answer 9

ya I did that, but I just wanted to make sure i got the right answers and simplified right?

Answer 10

a) with replacement: P(3 red)=343/1728 = 0.1984

Answer 11

without replacement: P(3 red)=7/44 = 0.159

Answer 12

what about the others?

Answer 13

B) with replacement: P(3 black)=(5/12)^3=125/1728

Answer 14

without replacement: P(3 black)=(5/12)(4/11)(3/10)=1/22

Answer 15

how did you get 1/22?

Answer 16

Calculator.

Answer 17

You can do it by hand though.

Answer 18

do you know how to do c?

Answer 19

Sorry, I had to go. In part (c), we want to get one red and two black marbles. There are three possibilities for this, red comes first, second or last. if R denotes red marbles and B denotes black marbles, then:
i) with replacement: P(one red and two black)=P(R B B)+P(B R B)+P(B B R)
=(7/12)(5/12)(5/12)+(5/12)(7/12)(5/12)+(5/12)(5/12)(7/12)
=3(7/12)(7/12)(5/12)= (use a calculator).

Answer 20

Try the same way and do the "without replacement" part.