3 boys are ages 4 , 6 and 7 respectively . 3 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 w , what is the difference between the probability that w is even and the probability that w is odd ?
age of boys w : 4 , 6 , 7 sum of ages taken 2 at a time : 10 , 1311 ages of girls : 5 , 8 , 9 sum of ages taken 2 at a time : 13 , 1714 9 combinations of sum between sets ( 10 , 1211 ) ( 13 , 1714 ) = 23 , 2724 - 16 , 3017 - 24 , 2825 prob ( even ) = 5 / 9 prob ( odd ) = 4 / 9 answer = 5 / 9 - 4 / 9 = 1 / 9
subtract(add(multiply(divide(const_1, 3), divide(const_1, 3)), multiply(divide(const_2, 3), divide(const_2, 3))), add(multiply(divide(const_1, 3), divide(const_2, 3)), multiply(divide(const_1, 3), divide(const_2, 3))))