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# simple probability quest

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Manager
Joined: 14 Dec 2004
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04 Mar 2005, 04:27
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Hi,

I can't get this simple probability question right. I just have the answers, no explanation. Here it is:

Two marbles are drawn in succession from a box containing 10red, 30white, 20blue, and 15 orange marbles, replacements being made after each drawing.

Find the probability that:
(1) They are either red or white or both (red and white)
(2) at most one is red
(3) only one is red

(1) 64/225
(2) 221/225
(3) 52/225
SVP
Joined: 03 Jan 2005
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04 Mar 2005, 07:04
(1) They are either red or white or both (red and white)
40/75*40/75=8/15*8/15=64/225

(2) at most one is red
Doesn't this mean both cannot be red?
1-10/75*10/75=1-2/15*2/15=1-4/225=221/225

(3) only one is red
First one is red, or the second one is red
(10/75*65/75)*2 = 2/15*13/15*2=52/225
Director
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04 Mar 2005, 07:17
what is wrong with this for (1)?

(10/75 * 10/75) + (30/75 * 30/75) + (10/75 * 30/75)

(R AND R) (W AND W) (R AND W)

= 52/225
SVP
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04 Mar 2005, 07:35
You are missing (W and R).
It should be:
(10/75 * 10/75) + (30/75 * 30/75) + (10/75 * 30/75)*2
= 64/225
Director
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04 Mar 2005, 07:37
Do you mean W and R is not the same as R and W?
SVP
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04 Mar 2005, 07:41
Exactly. Orders matter this time. First draw is R and second is W is a different outcome from first draw is W and second is R.
Intern
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04 Mar 2005, 07:42
Folaa3 wrote:
what is wrong with this for (1)?

(10/75 * 10/75) + (30/75 * 30/75) + (10/75 * 30/75)

(R AND R) (W AND W) (R AND W)

= 52/225

You forgot the (W and R) possibility, so you should add 12/225.
Manager
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04 Mar 2005, 08:20
(I) Both are red or both are white or one white the other red:

10/75*10/75 + 30/75*30/75 + 10/75* 30/75 + 30/75*10/75 = 64/225

(II) at most one is red:
(a) none is red
65/75*65/75= 4225/5625
(b) only one is red:
When it is RW :
10/75*65/75= 650/5625
When it is WR "
65/75 *10/75 = 650/5625

Adding the above prob = 221/225

(III)Only one is red:
RW: 10/75*65/75 = 650/5625
WR: 65/75*10/75 = 650/5625

04 Mar 2005, 08:20
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