A box contains 100 balls

A box contains 100 balls, numbered from 1 to 100. If five balls are selected at random and with replacement from the box, what is the probability that the sum of the five numbers on the balls selected from the box will be odd?

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by GMATGuruNY » Sat Sep 03, 2016 2:25 am

nahid078 wrote:A box contains 100 balls, numbered from 1 to 100. If five balls are selected at random and with replacement from the box, what is the probability that the sum of the five numbers on the balls selected from the box will be odd?

Ways to get an ODD sum:
1 odd, 4 even
3 odd, 2 even
5 odd

Ways to get an EVEN sum:
1 even, 4 odd
3 even, 2 odd
5 even

Since the number of ways in each case is THE SAME:
The probability of getting an odd sum = 1/2.
The probability of getting an even sum = 1/2.

The correct answer is [spoiler]1/2[/spoiler].

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