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A box contains 6 black balls and 4 white balls. If two balls are selec

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Bunuel
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A box contains 6 black balls and 4 white balls. If two balls are selec [#permalink] New post   18 Oct 2018, 01:41
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A box contains 6 black balls and 4 white balls. If two balls are selected at random without replacement, what is the probability that both balls are white?

A. 7/90
B. 3/25
C. 2/15
D. 4/25
E. 4/9
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Re: A box contains 6 black balls and 4 white balls. If two balls are selec [#permalink] New post   18 Oct 2018, 03:06
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Bunuel wrote:
A box contains 6 black balls and 4 white balls. If two balls are selected at random without replacement, what is the probability that both balls are white?

A. 7/90
B. 3/25
C. 2/15
D. 4/25
E. 4/9


The probability of both balls are white = 2C4/ 2C10 = 2/15

Hence, choice C is the answer
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Re: A box contains 6 black balls and 4 white balls. If two balls are selec [#permalink] New post   18 Oct 2018, 03:57
OA:C

Probability that both ball are white\(= \frac{C(4,2)}{C(10,2)}= \frac{4!}{2!2!}*\frac{2!8!}{10!}=\frac{4*3}{2*1}*\frac{2*1}{10*9}=\frac{2}{15}\)
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Re: A box contains 6 black balls and 4 white balls. If two balls are selec [#permalink] New post   19 Oct 2018, 15:25
Expert Reply
Bunuel wrote:
A box contains 6 black balls and 4 white balls. If two balls are selected at random without replacement, what is the probability that both balls are white?

A. 7/90
B. 3/25
C. 2/15
D. 4/25
E. 4/9


There are 10 balls in the box. The probability that the first ball drawn will be white is 4/10, and the probability that the second ball will also be white is 3/9. Thus, the probability of selecting two white balls, without replacement, is 4/10 x 3/9 = 2/5 x 1/3 = 2/15.

Answer: C
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Re: A box contains 6 black balls and 4 white balls. If two balls are selec [#permalink] New post   22 Oct 2018, 02:53
Bunuel wrote:
A box contains 6 black balls and 4 white balls. If two balls are selected at random without replacement, what is the probability that both balls are white?

A. 7/90
B. 3/25
C. 2/15
D. 4/25
E. 4/9


Ways of selecting 2 white balls = 4C2
probability of selecting 2 white balls= 4C2/10C2 =2/15

Option C is the answer.
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Re: A box contains 6 black balls and 4 white balls. If two balls are selec [#permalink] New post   22 Aug 2020, 13:59
Bunuel wrote:
A box contains 6 black balls and 4 white balls. If two balls are selected at random without replacement, what is the probability that both balls are white?

A. 7/90
B. 3/25
C. 2/15
D. 4/25
E. 4/9


1st pick
P(1st white ball) = \(\frac{4}{10}\)

2nd pick (since without replacement, there are only 3 white balls and 9 total number of balls)
P(2nd white ball) = \(\frac{3}{9}\)

P(2 white balls) = \(\frac{4}{10}\) * \(\frac{3}{9}\) = \(\frac{2}{15}\)
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Re: A box contains 6 black balls and 4 white balls. If two balls are selec [#permalink]
22 Aug 2020, 13:59
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