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# If a number is selected at random from a set of 6 distinct integers

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Math Expert
Joined: 02 Sep 2009
Posts: 61301
If a number is selected at random from a set of 6 distinct integers  [#permalink]

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26 Nov 2019, 00:33
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25% (medium)

Question Stats:

73% (01:09) correct 27% (01:14) wrong based on 55 sessions

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If a number is selected at random from a set of 6 distinct integers, what is the probability that the number is odd or prime?

(1) The probability of the number being odd is $$\frac{1}{6}$$.
(2) The probability of the number being prime is $$\frac{1}{3}$$.

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Joined: 19 Oct 2018
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Location: India
Re: If a number is selected at random from a set of 6 distinct integers  [#permalink]

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26 Nov 2019, 02:24
Statement 1-
There is 5 even numbers and 1 odd number

There can be 0,1 or 2 prime numbers

Insufficient

Statement 2-
There are 2 prime numbers; we will have at least 1 odd number

Insufficient

Combining both statements
We have 2 prime numbers (one odd and one even) and we have only 1 odd number, which is prime too.

Sufficient

Bunuel wrote:
If a number is selected at random from a set of 6 distinct integers, what is the probability that the number is odd or prime?

(1) The probability of the number being odd is $$\frac{1}{6}$$.
(2) The probability of the number being prime is $$\frac{1}{3}$$.

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Joined: 24 Nov 2016
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Location: United States
Re: If a number is selected at random from a set of 6 distinct integers  [#permalink]

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26 Nov 2019, 03:41
Bunuel wrote:
If a number is selected at random from a set of 6 distinct integers, what is the probability that the number is odd or prime?

(1) The probability of the number being odd is $$\frac{1}{6}$$.
(2) The probability of the number being prime is $$\frac{1}{3}$$.

(1) The probability of the number being odd is $$\frac{1}{6}$$. insufic

odd/6=1/6, one odd and five even: {1,2,4,6,8,10}; (odd,prime)/6 = 1/6
odd/6=1/6, one odd and five even: {2,3,4,6,8,10}; (odd,prime)/6 = 2/6

(2) The probability of the number being prime is $$\frac{1}{3}$$. insufic

prime/6=1/3: two primes {1,2,3,6,8,10}; (odd,prime)/6 = {1,2,3}/6 = 3/6
prime/6=1/3: two primes: {2,3,4,6,8,10}; (odd,prime)/6 = {2,3}/6

(1&2) sufic

Only even prime number is 2, the others are odd;
If there is only one odd, and two primes, then there is one odd prime and one even prime;
{odd,prime}/6=2/6=1/3

Ans (C)
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Joined: 08 Jan 2019
Posts: 4
Re: If a number is selected at random from a set of 6 distinct integers  [#permalink]

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26 Nov 2019, 05:15
As we don't know which distinct numbers are in the set, to know the possibility of the number being odd or prime we need to know more about which numbers are in the set i.e. the range.

Statement 1:
The probability of the number being odd is 1/6.
This doesn't tell us anything about the probability of the number being prime. There are many odd numbers that are prime.

Statement 2:
The probability of the number being prime is 1/3.
This tell us that most of the numbers are odd, except the number two which is prime and even. So there are still multiple outcomes.

Both statements together gives us the information we need to solve the probability for odd or prime.

C IMO
Re: If a number is selected at random from a set of 6 distinct integers   [#permalink] 26 Nov 2019, 05:15
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