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What is the probability that one of the two integers

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Senior Manager
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What is the probability that one of the two integers [#permalink]

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New post 08 Aug 2007, 05:30
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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)

(A) 0.06
(B) 0.12
(C) 0.15
(D) 0.18
(E) 0.20
[Reveal] Spoiler: OA

Last edited by Harley1980 on 08 Jul 2015, 13:02, edited 1 time in total.
OA added
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Re: What is the probability that one of the two integers [#permalink]

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New post 08 Aug 2007, 06:05
I'm going with A on this one.

Chance of picking a prime number:

2/10 (23 and 29 are the only prime numbers out of 20-29)

Chance of picking a multiple of 3:

3/10 (21, 24, 27 are the only multiples of 3 out of 20-29)

so 2/10 * 3/10 = 6/100 or .06


I like the line about the numbers being selected independently i.e. they can be equal.

by definition you'll never have a number that can be both prime and a multiple of 3!
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Re: What is the probability that one of the two integers [#permalink]

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New post 08 Aug 2007, 06:09
Vlad77 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)

(A) 0.06
(B) 0.12
(C) 0.15
(D) 0.18
(E) 0.20


I get A for this.

P(prime no.) = 2/10 (only 23 and 29)
P(multiple of 3) = 3/10 (only 21, 24 and 27)

So, p = 0.2*0.3 = 0.06.
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Re: What is the probability that one of the two integers [#permalink]

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New post 08 Aug 2007, 08:01
Vlad77 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)

(A) 0.06
(B) 0.12
(C) 0.15
(D) 0.18
(E) 0.20


Another A.
Total = 10.
Prime are 23, 29 => Prob = 2/10
Multiple of three are 21, 24, 27 => Prob = 3/10
2/10 * 3/10 = 6/100 = 0.06
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Re: What is the probability that one of the two integers [#permalink]

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New post 11 Aug 2007, 23:26
The official explanation:
Prime integers: 23 and 29. Multiples of 3: 21, 24, and 27. The probability that the first number is prime while the second is multiple of 3 = 2/10*3/10=0.06.
The probability that the first number is a multiple of 3 while the second is prime = 3/10*2/10=0.06.
The probability that one of the two integers is prime and the other is multiple of 3=0.06+0.06=0.12
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Re: What is the probability that one of the two integers [#permalink]

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New post 14 Aug 2007, 03:33
Hi,

I was wondering why when we select the first prime, the number of possibilities dont get reduced by one.
If I say it diffrently, why the solution is not (2/10)*(3/9)?

Thanks for your great posts!
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Re: What is the probability that one of the two integers [#permalink]

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New post 14 Aug 2007, 05:08
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The numbers are selected independently of each other....which means you pick a number and put it back.
Attempt 1 - Pick either prime number or a number divisible by 3: P = (2/10)*(3/10) = 0.06
Attempt 2 - Pick either prime number or a number divisible by 3: P = (2/10)*(3/10) = 0.06

0.06+0.06 = 0.12 (B)
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Re: What is the probability that one of the two integers [#permalink]

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New post 14 Aug 2007, 07:45
bramasu wrote:
The numbers are selected independently of each other....which means you pick a number and put it back.
Attempt 1 - Pick either prime number or a number divisible by 3: P = (2/10)*(3/10) = 0.06
Attempt 2 - Pick either prime number or a number divisible by 3: P = (2/10)*(3/10) = 0.06

0.06+0.06 = 0.12 (B)


but the questions asks

Quote:
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?


which means you can have a .06 probability of picking one or the other on the first pick...but the second pick HAS to be the one you didn't choose. Like if you chose a prime the first time around, you would HAVE to choose a multiple of 3 the second time. Given your equation you could choose two primes or two multiples of 3, which is not what the question is asking.

I don't know if the answer is A now, but I don't think your equation follows instructions either. Anyone else agree with this or am I missing something?
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Re: What is the probability that one of the two integers [#permalink]

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New post 14 Aug 2007, 11:58
P(Prime) * P(Multiple Of 3) + P(Multiple of 3) * P(Prime)
=2/10 * 3/9 + 3/10 * 2/9
=1/15 + 1/15
=2/15
=0.1333
= 0.12 (approx)
B
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Re: What is the probability that one of the two integers [#permalink]

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New post 14 Aug 2007, 16:02
Recent posting with the same trick...

http://www.gmatclub.com/phpbb/viewtopic.php?t=50464
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Re: What is the probability that one of the two integers [#permalink]

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New post 14 Aug 2007, 18:02
It would have to be B, because they can be picked in either order. So there is a .06 probability of picking a prime, then a multiple of 3, + a .06 probability of picking a multiple of 3, then a prime. .06 + .06 = .12
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Re: What is the probability that one of the two integers [#permalink]

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New post 14 Aug 2007, 21:25
B is correct as your first pick can be prime or multiple of 3.
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Re: What is the probability that one of the two integers [#permalink]

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Re: What is the probability that one of the two integers   [#permalink] 23 Feb 2017, 09:40
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