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# For a certain game, three numbers are drawn, each from 1 to

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For a certain game, three numbers are drawn, each from 1 to [#permalink]  07 May 2012, 04:50
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For a certain game, three numbers are drawn, each from 1 to 10. A player can win if the product of his or her three numbers is odd. Initially, the same number may be picked up to three times. Later, the rules are changed so that each number may only be picked once. Approximately how much does this reduce a person's probability of winning?

A. 0.04
B. 0.08
C. 0.1
D. 0.125
E. 0.5

I'm making some mistake while calculating the probability for the second part ,can someone explain the mistake here ?

For second part :

Total number of outcomes = 10*10*10=1000
Total number of favourable outcomes (i.e. picking 3 out 5 odd numbers ) = 5C3 = 10

Probability = 1/100 = 0.01
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Re: For a certain game, three numbers are drawn, each from 1 to [#permalink]  07 May 2012, 05:09
georgepaul0071987 wrote:
For a certain game, three numbers are drawn, each from 1 to 10. A player can win if the product of his or her three numbers is odd. Initially, the same number may be picked up to three times. Later, the rules are changed so that each number may only be picked once. Approximately how much does this reduce a person's probability of winning?

A. 0.04
B. 0.08
C. 0.1
D. 0.125
E. 0.5

I'm making some mistake while calculating the probability for the second part ,can someone explain the mistake here ?

For second part :

Total number of outcomes = 10*10*10=1000
Total number of favourable outcomes (i.e. picking 3 out 5 odd numbers ) = 5C3 = 10

Probability = 1/100 = 0.01

The product of three numbers is odd if all three numbers are odd.

Initially P(OOO)=5/10*5/10*5/10=1/8;
Later P(OOO)=5/10*4/9*3/8=1/12;

The difference is 1/8-1/12=1/24=~0.04.

Answer: A.
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Re: For a certain game, three numbers are drawn, each from 1 to [#permalink]  07 May 2012, 07:10
Thanks for the quick response ! But could you explain where exactly I went wrong in my calculations for the 2nd probability ?

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Re: For a certain game, three numbers are drawn, each from 1 to   [#permalink] 07 May 2012, 07:10
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