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Math Expert V
Joined: 02 Sep 2009
Posts: 59590

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Difficulty:   25% (medium)

Question Stats: 79% (01:15) correct 21% (01:09) wrong based on 91 sessions

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Two sets are defined as follows:

$$A = \{2, 3, 4, 4, 4\}$$

$$B = \{0, 1, 2\}$$

If a number is taken from set $$A$$ at random and another number is taken from set $$B$$ at random, what is the probability that the sum of these numbers is a prime integer?

A. $$\frac{1}{15}$$
B. $$\frac{2}{15}$$
C. $$\frac{5}{15}$$
D. $$\frac{7}{15}$$
E. $$\frac{9}{15}$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 59590

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Official Solution:

Two sets are defined as follows:

$$A = \{2, 3, 4, 4, 4\}$$

$$B = \{0, 1, 2\}$$

If a number is taken from set $$A$$ at random and another number is taken from set $$B$$ at random, what is the probability that the sum of these numbers is a prime integer?

A. $$\frac{1}{15}$$
B. $$\frac{2}{15}$$
C. $$\frac{5}{15}$$
D. $$\frac{7}{15}$$
E. $$\frac{9}{15}$$

The total # of outcomes is $$5*3=15$$.

Now, as set $$B$$ is smaller, then work with it:

0 can be added to 2 or to 3 to get a prime: $$1+1=2$$ cases;

1 can be added to 2 or to either of three 4's to get a prime: $$1+3=4$$ cases;

2 can be added only to 3 to get a prime: 1 case.

So, the total # of favorable outcomes is $$2+4+1=7$$. $$P=\frac{\text{favorable}}{\text{total}}=\frac{7}{15}$$.

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Intern  Joined: 06 Sep 2008
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Can someone please explain why we do not consider (2,3) & (3,2) as two separate possible outcomes and count them both while calculating the probability, similar to what we do when we roll two dice and calculate, the sum of both dice to be say 8.
Thanks,
Srinivas
Math Expert V
Joined: 02 Sep 2009
Posts: 59590

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srivelivala wrote:
Can someone please explain why we do not consider (2,3) & (3,2) as two separate possible outcomes and count them both while calculating the probability, similar to what we do when we roll two dice and calculate, the sum of both dice to be say 8.
Thanks,
Srinivas

You don't have a 3 in set B.
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Intern  Joined: 26 Sep 2014
Posts: 9
Location: India
Schools: IIMB (A)
GMAT 1: 700 Q50 V34 GPA: 3.2

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Bunuel wrote:
Official Solution:

Two sets are defined as follows:

$$A = \{2, 3, 4, 4, 4\}$$

$$B = \{0, 1, 2\}$$

If a number is taken from set $$A$$ at random and another number is taken from set $$B$$ at random, what is the probability that the sum of these numbers is a prime integer?

A. $$\frac{1}{15}$$
B. $$\frac{2}{15}$$
C. $$\frac{5}{15}$$
D. $$\frac{7}{15}$$
E. $$\frac{9}{15}$$

The total # of outcomes is $$5*3=15$$.

Now, as set $$B$$ is smaller, then work with it:

0 can be added to 2 or to 3 to get a prime: $$1+1=2$$ cases;

1 can be added to 2 or to either of three 4's to get a prime: $$1+3=4$$ cases;

2 can be added only to 3 to get a prime: 1 case.

So, the total # of favorable outcomes is $$2+4+1=7$$. $$P=\frac{\text{favorable}}{\text{total}}=\frac{7}{15}$$.

How come there are 15 total possible outcomes... when there are only 3 distinct elements in set A.
I believe the possible outcomes should only be 9.
plz correct me if im wrong
Math Expert V
Joined: 02 Sep 2009
Posts: 59590

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jamesav wrote:
Bunuel wrote:
Official Solution:

Two sets are defined as follows:

$$A = \{2, 3, 4, 4, 4\}$$

$$B = \{0, 1, 2\}$$

If a number is taken from set $$A$$ at random and another number is taken from set $$B$$ at random, what is the probability that the sum of these numbers is a prime integer?

A. $$\frac{1}{15}$$
B. $$\frac{2}{15}$$
C. $$\frac{5}{15}$$
D. $$\frac{7}{15}$$
E. $$\frac{9}{15}$$

The total # of outcomes is $$5*3=15$$.

Now, as set $$B$$ is smaller, then work with it:

0 can be added to 2 or to 3 to get a prime: $$1+1=2$$ cases;

1 can be added to 2 or to either of three 4's to get a prime: $$1+3=4$$ cases;

2 can be added only to 3 to get a prime: 1 case.

So, the total # of favorable outcomes is $$2+4+1=7$$. $$P=\frac{\text{favorable}}{\text{total}}=\frac{7}{15}$$.

How come there are 15 total possible outcomes... when there are only 3 distinct elements in set A.
I believe the possible outcomes should only be 9.
plz correct me if im wrong

Number 4 is in set A three times. So, the probability of picking 4 is higher, than the probability of picking 2 or 3, which should be taken into account.
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Intern  B
Joined: 29 Nov 2016
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favourable outcome are (2,0) (2,1)
(3,0) (3,2)
(4,1)
(4,1)
(4,1)
hence probability is 7/15
but i considered all (4,1) is similar then my total favourable outcome is 5. hence i marked ans 5/15.

plz clarify.
Math Expert V
Joined: 02 Sep 2009
Posts: 59590

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digvijay99 wrote:
favourable outcome are (2,0) (2,1)
(3,0) (3,2)
(4,1)
(4,1)
(4,1)
hence probability is 7/15
but i considered all (4,1) is similar then my total favourable outcome is 5. hence i marked ans 5/15.

plz clarify.

Since there are three 4's in A, then the probability of getting (4, 1) is greater than if there were just one 4.
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Intern  B
Joined: 07 Jan 2017
Posts: 5

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1
Hi Bunuel,

Only elements of type {A,B} are considered or {B,A} are considered. Why not both?
Type {A,B}:
(2,0) (2,1)
(3,0) (3,2)
(4,1)
(4,1)
(4,1)
Type {B,A}
(0,2)(0,3)..like this we will again get here 7 possible outcomes. I didn't understand why we haven't considered both types of sets. Could you please explain?
Intern  B
Joined: 06 Jun 2018
Posts: 42
Location: India
Schools: IIMA PGPX"20 (D)
GMAT 1: 640 Q47 V30 GMAT 2: 540 Q42 V22 GPA: 3.7

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Bunuel,

I got the answer correct at first place but I used guess. What I was trying before I guess is : P = X/N so N = Total number of ways to select 2 numbers out of 8 is 2C8 and X= Ways to pair prime number and select 2 out of it so it is 2C7 and after calculations it gives me 3/4. Re: M08-05   [#permalink] 06 Oct 2018, 05:11
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# M08-05

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