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# Set S consists of all prime integers less than 10. If a

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Set S consists of all prime integers less than 10. If a [#permalink]  09 Sep 2008, 10:07
Set S consists of all prime integers less than 10. If a number is selected from set S at random and then another number, not necessarily different, is selected from set S at random, what is the probability that the sum of these numbers is odd?

1/8
1/6
3/8
1/2
5/8

my approach was , the three pairs to be selected for odd is 2&3, 2&5, 2&7. i.e 3 no. pairs
possible cases = 4nos. taken 2 at a time = 4c2 = 4*3/2*1=6.
so
total =3/6 = 1/2.
what is wrong??
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Re: sum of nos is odd- probability [#permalink]  09 Sep 2008, 10:22
I think, favorable outcome will consist of
23, 25, 27
32, 35, 37
52, 53, 57
72, 73, 75

and total outcome will be
22, 23, 25, 27
33, 32, 35, 37
55, 52, 53, 57
77, 72, 73, 75

and the probability should be 12/16 = 3/4....but I do not find that in the answer choice....

Calling x2suresh, et al....for rescue.
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Re: sum of nos is odd- probability [#permalink]  09 Sep 2008, 10:24
You know what....I realized my mistake.

Favorable outcome will only be
23, 25, 27
32,
52,
72

and hence the probability will be 6/16 = 3/8.

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Re: sum of nos is odd- probability [#permalink]  09 Sep 2008, 10:29
arjtryarjtry wrote:
Set S consists of all prime integers less than 10. If a number is selected from set S at random and then another number, not necessarily different, is selected from set S at random, what is the probability that the sum of these numbers is odd?

1/8
1/6
3/8
1/2
5/8

my approach was , the three pairs to be selected for odd is 2&3, 2&5, 2&7. i.e 3 no. pairs
possible cases = 4nos. taken 2 at a time = 4c2 = 4*3/2*1=6.
so
total =3/6 = 1/2.
what is wrong??

Prime no's less than 10 = (2,3,5,7)
total cases is 4*4 = 16

Favourible cases = (2,3) (2,5) (2,7) and vice versa = 6 cases

P(Sum odd) = 6/16 = 3/8
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Re: sum of nos is odd- probability [#permalink]  09 Sep 2008, 10:32
scthakur wrote:
You know what....I realized my mistake.

Favorable outcome will only be
23, 25, 27
32,
52,
72

and hence the probability will be 6/16 = 3/8.

you got it.

think there are two buckets.
bucket -A [2 ,3,5,7]
bucket -B [2, 3,5,7]

sum will be odd only when combine odd+even.

when you select 2 from bucket A you have 3 options to select odd numbers from bucket B
=3
when you select 2 from bucket B you have 3 options to select odd numbers from bucket A

p = 3+3/(4*4)=3/8
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Re: sum of nos is odd- probability   [#permalink] 09 Sep 2008, 10:32
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