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# For a lottery, three numbers are drawn, each from 1 to 40. A player ca

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Math Expert
Joined: 02 Sep 2009
Posts: 56275
For a lottery, three numbers are drawn, each from 1 to 40. A player ca  [#permalink]

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16 Aug 2018, 08:47
00:00

Difficulty:

95% (hard)

Question Stats:

39% (03:55) correct 61% (02:45) wrong based on 26 sessions

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For a lottery, three numbers are drawn, each from 1 to 40. 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 0.01
B 0.025
C 0.115
D 0.125
E 0.5

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Joined: 20 Feb 2015
Posts: 790
Concentration: Strategy, General Management
Re: For a lottery, three numbers are drawn, each from 1 to 40. A player ca  [#permalink]

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16 Aug 2018, 09:17
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Bunuel wrote:
For a lottery, three numbers are drawn, each from 1 to 40. 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 0.01
B 0.025
C 0.115
D 0.125
E 0.5

case 1 - same number can be picked up to 3 times
the product will be odd , if and only if all 3 numbers drawn are odd because even*odd=even

total odd numbers from 1-40= 20
favorable outcome = 20*20*20
total no of outcomes = 40*40*40
probability( case 1) = 1/8

case 2 - each number may be picked once

favorable outcomes = 20*19*18
total no of outcomes =40*39*38
probability(case 2) = 3/26

difference = 1/8-3/26 = ~0.01
A
Re: For a lottery, three numbers are drawn, each from 1 to 40. A player ca   [#permalink] 16 Aug 2018, 09:17
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