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# A bag contains 3 white, 4 black, and 2 red marbles. Two marb

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A bag contains 3 white, 4 black, and 2 red marbles. Two marb [#permalink]  15 Sep 2017, 07:47
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Question Stats:

57% (01:10) correct 42% (01:00) wrong based on 19 sessions

A bag contains 3 white, 4 black, and 2 red marbles. Two marbles are drawn from the bag. If replacement is not allowed, what is the probability that the second marble drawn will be red?

A. $$\frac{1}{36}$$

B. $$\frac{1}{12}$$

C. $$\frac{7}{36}$$

D. $$\frac{2}{9}$$

E. $$\frac{7}{9}$$
[Reveal] Spoiler: OA

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Re: A bag contains 3 white, 4 black, and 2 red marbles. Two marb [#permalink]  21 Sep 2017, 05:13
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The probability of extracting a red marble in the second draw is equal to the probability of extracting whatever marble in the first draw times the probability of extracting a red marble in the second draw, i.e. 1*2/9 = 2/9. Answer D!
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Re: A bag contains 3 white, 4 black, and 2 red marbles. Two marb [#permalink]  04 Mar 2018, 05:40
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The scenario of getting a red marble in the second draw could be like this:
1) no red in first draw and a red in the second draw
2) a red in the first draw and a red in the second draw

1) (7/9)*(2/8)=7/36
2) (2/9)*(1/8)=1/36

So, the probability that the second marble is drawn will be red = (7/36)+(1/36)=2/9

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Re: A bag contains 3 white, 4 black, and 2 red marbles. Two marb [#permalink]  13 May 2018, 16:45
Expert's post
Carcass wrote:

A bag contains 3 white, 4 black, and 2 red marbles. Two marbles are drawn from the bag. If replacement is not allowed, what is the probability that the second marble drawn will be red?

A. $$\frac{1}{36}$$

B. $$\frac{1}{12}$$

C. $$\frac{7}{36}$$

D. $$\frac{2}{9}$$

E. $$\frac{7}{9}$$

If a red marble is selected first and a red marble is selected second, the probability is:

2/9 x 1/8 = 2/72

If a red marble is not selected first and a red marble is selected second, the probability is:

7/9 x 2/8 = 14/72

So the overall probability is 2/72 + 14/72 = 16/72 = 2/9.

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Re: A bag contains 3 white, 4 black, and 2 red marbles. Two marb   [#permalink] 13 May 2018, 16:45
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