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A box contains 1 blue ball, 1 green ball, 1 yellow ball

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BrentGMATPrepNow
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A box contains 1 blue ball, 1 green ball, 1 yellow ball [#permalink] New post   10 Jan 2017, 12:41
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A box contains 1 blue ball, 1 green ball, 1 yellow ball, and 2 red balls.
Three balls are randomly selected (one after the other) without replacement.
What is the probability that the 2nd ball is NOT red and the 3rd ball is yellow?

A) 1/30
B) 1/20
C) 1/10
D) 3/20
E) 1/5

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C
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vitaliyGMAT
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Re: A box contains 1 blue ball, 1 green ball, 1 yellow ball [#permalink] New post   10 Jan 2017, 13:27
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GMATPrepNow wrote:
A box contains 1 blue ball, 1 green ball, 1 yellow ball, and 2 red balls.
Three balls are randomly selected (one after the other) without replacement.
What is the probability that the 2nd ball is NOT red and the 3rd ball is yellow?

A) 1/30
B) 1/20
C) 1/10
D) 3/20
E) 1/5

* Kudos for all correct solutions


Hi

The second picked ball can't be red and the first and second also can't be yellow, otherwise our probability of the third ball to be yellow will be 0. Hence there are only three possible cases:

Blue Green Yellow + Green Blue Yellow + Red (Blue/Green) Yellow (or 4 if we write blue and green for the second ball separately)

\(\frac{1}{5}*\frac{1}{4}*\frac{1}{3} + \frac{1}{5}*\frac{1}{4}*\frac{1}{3} + \frac{2}{5}*\frac{2}{4}*\frac{1}{3} = \frac{1+1+4}{60} = \frac{6}{60} = \frac{1}{10}\)

Answer C.
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BrentGMATPrepNow
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Re: A box contains 1 blue ball, 1 green ball, 1 yellow ball [#permalink] New post   11 Jan 2017, 08:13
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GMATPrepNow wrote:
A box contains 1 blue ball, 1 green ball, 1 yellow ball, and 2 red balls.
Three balls are randomly selected (one after the other) without replacement.
What is the probability that the 2nd ball is NOT red and the 3rd ball is yellow?

A) 1/30
B) 1/20
C) 1/10
D) 3/20
E) 1/5


First of all, it's useful to recognize that P(2nd ball is NOT red and the 3rd ball is yellow) is the SAME as P(1st ball is NOT red and the 2nd ball is yellow)

P(1st ball is NOT red AND the 2nd ball is yellow) = P(1st ball is NOT red) x P(the 2nd ball is yellow)
= 2/5 x 1/4
= 1/10
= C

Aside: The first probability, P(1st ball is NOT red), equals 2/5, because there are 5 balls to choose from, and we cannot choose a red ball (because that's not allowed) AND we cannot choose a yellow ball (because, that ball must be available for the next selection). So, of the 5 possible balls to choose from on the first selection, only 2 balls (the blue and green balls) are permissible.

Cheers,
Brent
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Re: A box contains 1 blue ball, 1 green ball, 1 yellow ball [#permalink] New post   13 Jan 2017, 04:07
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GMATPrepNow wrote:
A box contains 1 blue ball, 1 green ball, 1 yellow ball, and 2 red balls.
Three balls are randomly selected (one after the other) without replacement.
What is the probability that the 2nd ball is NOT red and the 3rd ball is yellow?

A) 1/30
B) 1/20
C) 1/10
D) 3/20
E) 1/5

* Kudos for all correct solutions

As last ball must be yellow,
Ball 3 can be picked in only 1 way
2 ball cannot be red so only 2 options are left(total-1 yellow-2 red)
1st ball can be picked in3 ways(2red+1 b/g)
So total ways is 3*2*1=6
Now total number of ways without any conditions is =5!/2!=60
Required probability =6/60=1/10
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A box contains 1 blue ball, 1 green ball, 1 yellow ball [#permalink] New post   17 Feb 2019, 09:41
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probability: 3/3 * 2/4 * 1/5
Starting from the right slot because it's easier.
1 yellow out of 5 = 1/5
2 non red (green or blue) out of remaining 4 = 2/4 = 1/2
any of the 3 remaining balls (red and green or blue) = 3/3
1*1/2*1/5 = 1/10

combinations: 3C1*2C1*1C1 / 5P3
denominator is 5P3 = 60, we use permutations because order matters
Starting from the right of the 3 slots, ways to choose 1 yellow = 1C1
ways to choose a non-red from remaining 4 = 2C1
ways to choose a remaining ball out of 3 = 3C1
numerator = 3*2*1
3*2*1/60 = 6/60 = 1/10
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A box contains 1 blue ball, 1 green ball, 1 yellow ball [#permalink] New post   28 Feb 2019, 04:56
GMATPrepNow wrote:

First of all, it's useful to recognize that P(2nd ball is NOT red and the 3rd ball is yellow) is the SAME as P(1st ball is NOT red and the 2nd ball is yellow)

P(1st ball is NOT red AND the 2nd ball is yellow) = P(1st ball is NOT red) x P(the 2nd ball is yellow)
= 2/5 x 1/4
= 1/10
= C

Aside: The first probability, P(1st ball is NOT red), equals 2/5, because there are 5 balls to choose from, and we cannot choose a red ball (because that's not allowed) AND we cannot choose a yellow ball (because, that ball must be available for the next selection). So, of the 5 possible balls to choose from on the first selection, only 2 balls (the blue and green balls) are permissible.

Cheers,
Brent


On the highlighted text, is this always true? Applicable in all cases?
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adewale223
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Re: A box contains 1 blue ball, 1 green ball, 1 yellow ball [#permalink] New post   07 Nov 2022, 10:32
Case 1

First red, second blue/green, third yellow

2/5 x 2/4 x 1/3

= 1/15

Second case

Blue or green, second one of blue/ green and yellow

2/5 x 1/4 x 1/3
1/30.

Therefore

1/15 + 1/30


1/10.

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Re: A box contains 1 blue ball, 1 green ball, 1 yellow ball [#permalink]
07 Nov 2022, 10:32
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