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There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar

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There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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New post 05 Dec 2014, 07:44
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Tough and Tricky questions: Probability.



There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability that at least one will be orange?

A) 7/10
B) 3/5
C) 2/5
D) 3/10
E) 1/10

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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New post 05 Dec 2014, 10:30
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The probability that at least one marble picked is orange is equal to 1 - the probability that zero orange marbles are picked. This probability is basically saying that we're first picking one of the three blue marbles from 5 total marbles and then picking one of two blue marbles from a total of four marbles. Assume that we're not replacing any marbles back into the bag.

This means P = 1 - 3/5*2/4 = 1 - 6/20 = 1 - 3/10 = 7/10.

Choice A
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Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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New post 06 Dec 2014, 07:09
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1st ball orange and 2nd ball orange =2/5*1/4=1/10
1st ball blue and 2nd ball orange =3/5*2/4=3/10
1st ball orange and 2nd ball blue= 2/5*3/4=3/10

so total probability = 1/10+3/10+3/10=7/10
Hope this is clear.
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Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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New post 05 Dec 2014, 13:59
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There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability that at least one will be orange?

A) 7/10
B) 3/5
C) 2/5
D) 3/10
E) 1/10


Method 1

Probability that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue)*P(Second Marble is Blue) = 1- (3/5)(2/4) = 7/10

Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10

Method 3

Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10

Answer : A
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Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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New post 05 Dec 2014, 08:21
Probability of the first ball being orange = 2/5
The first all is not replaced, hence the total number of balls for the second pick = 1/4
Therefore the total probability is 2/5 x 1/4 = 1/10

Hence E
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Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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New post 06 Dec 2014, 00:16
Yes the above explanation is right. I misread :(
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Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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New post 08 Dec 2014, 06:13
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Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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New post 28 Aug 2018, 01:43
Bunuel wrote:

Tough and Tricky questions: Probability.



There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability that at least one will be orange?

A) 7/10
B) 3/5
C) 2/5
D) 3/10
E) 1/10

Kudos for a correct solution.

Source: Chili Hot GMAT



the probability of none of the marble will be orange is \(\frac{3}{5}\frac{2}{4}\)=\(\frac{3}{10}\)
the probability that at least one will be orange 1-\(\frac{3}{10}\) = \(\frac{7}{10}\)
the answer is A
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There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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New post 28 Aug 2018, 08:08
That was eazy!


(2C1*3C2+2C2)/5C2 = 7/10

Hope it's clear!
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There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar   [#permalink] 28 Aug 2018, 08:08
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