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M22-08

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Manager
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M22-08 [#permalink]

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New post 01 Mar 2013, 05:58
What is the probability that one of the two integers randomly selected from range 20-29 is prime and the other is a multiple of 3?

(The numbers are selected independently of each other, i.e. they can be equal)

0.06
0.12
0.15
0.18
0.20

I got the answer as 0.06 but im not sure why its wrong.
Director
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Re: M22-08 [#permalink]

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New post 01 Mar 2013, 07:37
shreerajp99 wrote:
What is the probability that one of the two integers randomly selected from range 20-29 is prime and the other is a multiple of 3?

(The numbers are selected independently of each other, i.e. they can be equal)

0.06
0.12
0.15
0.18
0.20

I got the answer as 0.06 but im not sure why its wrong.


Probability that one integer is a prime number
prime numbers between 20-29 are 23,29
So probability is 2/10 = 0.2

Multiple of 3
Multiple's of 3 between 20 and 29 are 21,24,27
so 3/10

Probability of choosing one prime and one factor of 3= (probability of choosing prime first and factor of 3 second) + (Probability of choosing factor of 3 first and prime second)
= 2 * 0.2 *0.3 = 0.12

Answer is B
Hope if helps!
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Manager
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New post 01 Mar 2013, 07:53
Hi,

My question is why are we doing it twice?
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Director
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Re: M22-08 [#permalink]

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New post 01 Mar 2013, 08:00
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shreerajp99 wrote:
Hi,

My question is why are we doing it twice?


Because the sequence in which you choose does matter!
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Re: M22-08 [#permalink]

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New post 21 Mar 2013, 16:39
Another way to think of it is:
How many sets of 2 numbers can be formed such that one of them is prime and the other is a multiple of 3? it's twice of (no. of primes x no. of multiples of 3)=12
How many sets of 2 numbers can be formed from the pool of numbers you're allowed to choose from? it's 10x10=100
so probability =12/100=0.12
Re: M22-08   [#permalink] 21 Mar 2013, 16:39
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