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Three boys are ages 4, 6 and 7 respectively. Three girls are [#permalink]

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09 Dec 2012, 09:05

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68% (03:04) correct
33% (02:15) wrong based on 160 sessions

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Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is z, what is the difference between the probability that z is even and the probability that z is odd?

Re: Three boys are ages 4, 6 and 7 respectively. Three girls are [#permalink]

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09 Jul 2014, 06:00

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Re: Three boys are ages 4, 6 and 7 respectively. Three girls are [#permalink]

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13 Jul 2015, 11:06

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Please feel free to critique me here but this is how I solved.

Boys: 4, 6, 7 Girls: 5, 8, 9 Number of possible combinations of boys or girls = 3!/2! = 3 i.e. there is 3 possible combinations of girls and 3 of boys

Probability that sum of 2 boys ages is even = 1/3 [a] Probability that sum of 2 boys ages is odd = 2/3 [b] Probability that sum of 2 girls ages is even = 1/3 [c] Probability that sum of 2 girls ages is odd = 2/3 [d]

probability that sum of 2 girls and 2 boys is even = [a]*[c] + [b]*[d] = 5/9 [e] probability that sum of 2 girls and 2 boys is odd = [a]*[b] + [c]*[d] = 4/9 [f]

Therefore the differences in the probabilities is [e] - [f] = 1/9

No idea if this is correct or if it was dumb luck. I am struggling daily with this GMAT journey so would appreciate the feedback.
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