The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth-grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. If there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected atrandom is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.)
Let x be the number of left-handed female students and let y be the number of left-handed male students. Then the number of right handed female students will be 5x and the number of right-handed male students will be 9y. Since the total number of left-handed students is 18 and the total number of right-handed students is 122, the system of equations below must be satisfied.
Solving this system gives x = 10 and . Thus, 50 of the 122 right-handed students are female. Therefore, the probability that a right-handed student selected at random is female is , which to the nearest thousandth is 0.410. Choices B, C, and D are incorrect and may be the result of incorrect calculation of the missing values in the table.