A Bag contains 100 balloons numbered from 1 to 100 If three balloons are selected at random and with...........

Quantitative Aptitude ( CCS) Probability

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

1/2

1/4

2/3

1/5

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Explanation:

P(odd) =P (even) = 1/2 (because there are 50 odd and 50 even numbers)
Sum of the three numbers can be odd only under the following 4 scenarios:
Odd + Odd + Odd = 1/2*1/2*1/2 =1/8
Odd + Even + Even =1/2*1/2*1/2 =1/8
Even + Odd + Even = 1/2*1/2*1/2 =1/8
Even + Even + Odd =1/2*1/2*1/2 =1/8
Adding all 1/8+1/8+1/8+1/8=4/8==>1/2.

Hence, option 1 is the correct answer.