Question 218189: Five balls are numbered with the integers 1 through 5 and placed in a jar. Three are drawn without replacement. What is the probability that the sum of the three integers on the balls is odd? Express your answer as a common fraction.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! integers 1 through 5
sum of 3 numbers is odd if:
2 are even and 1 is odd
3 are odd
no other combination will work.
3 even gives even
2 odd and 1 even gives even
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there are 3 odds in there (1,3,5)
there are 2 evens in there (2,4)
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PROBABILITY OF GETTING 2 EVENS AND 1 ODD
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probability of getting 2 evens and 1 odd are:
2/5 * 1/4 * 3/3
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you can get this in 3 ways.
they would be:
first draw is odd, second draw is odd, third draw is even.
first draw is odd, second draw is even, third draw is odd.
first draw is even, second draw is odd, third draw is odd.
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the probability of each one of these occurrences is the same.
it is 2/5 * 1/4 * 3/3 = .1
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the total probability for getting 2 even and 1 odd is 3 * .1 = .3
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PROBABILITY OF GETTING 3 ODDS
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The probability for getting 3 odds are:
3/5 * 2/4 * 1/3
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you can get this in 1 way.
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the total probability for getting 3 odds = .1
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PROBABILITY OF GETTING 3 ODDS OR 2 EVENS AND 1 ODD
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This equals .3 + .1 = .4
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You have a 40% probability of getting an odd number sum for 3 numbers drawn out of the numbers 1,2,3,4,5
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