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Math Expert V
Joined: 02 Sep 2009
Posts: 58396
There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 72% (01:19) correct 28% (01:31) wrong based on 213 sessions

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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

_________________
Intern  Status: Amat Victoria Curam
Joined: 13 Sep 2014
Posts: 24
Location: India
Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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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
Manager  Joined: 12 Sep 2014
Posts: 142
GMAT 1: 740 Q49 V41 GPA: 3.94
Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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2
1
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
Manager  Joined: 04 Oct 2013
Posts: 150
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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1
1
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

Intern  Status: Amat Victoria Curam
Joined: 13 Sep 2014
Posts: 24
Location: India
Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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Yes the above explanation is right. I misread Manager  Status: Applied
Joined: 02 May 2014
Posts: 125
Location: India
Concentration: Operations, General Management
GMAT 1: 690 Q47 V38 GPA: 3.35
WE: Information Technology (Computer Software)
Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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2
1
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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58396
Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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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 correct answer is A.
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Intern  B
Joined: 25 Jan 2013
Posts: 20
Concentration: Marketing, Strategy
GPA: 3.64
Re: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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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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pressing +1 kudos is a nice way to say thanks

Intern  B
Joined: 31 Jul 2018
Posts: 1
There are 5 marbles in a bag - 2 are orange and 3 are blue. If two mar  [#permalink]

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That was eazy!

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

Hope it's clear! 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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