The table shows the percentage of students in each of three grade levels, and the percentage who list basketball as their favorite sport.  Grade Percent in grade Percent of that grade who favor basketball 10th 41% 40% 11th 30% 35% 12th 29% 40% Total 100% (0.4)(0.41) + (0.35)(0.30) + (0.4)(0.29) = 0.385 or 38.5% What is the probability that the student is a 10th grader, given that basketball is the favorite sport listed, to the nearest percent?16404143

First, let's find out what percentage of the total group of students lists basketball as their favorite sport:
10th: .41 * .4 = 16.4% of the school are 10th grade ballers
11th: .30 * .35 = 10.5% of the school are 11th grade ballers
12th: .29 * .40 = 11.6% of the school are seniors who drain like Kobe
Total:                    38.5% of all students list basketball as their favorite sport. 

We divide the portion of 10th grade basketball fans by the total proportion of basketball fans:
16.4% ÷ 38.5% = 42.6%

There is a 42.6% chance that the student is a 10th grader, given that he/she is a basketball fan.