SOLUTION: A random sample of 250 students entering the university included 120 females, of whom 20 belonged to a minority group, 65 had averages over 80%, and 10 fit both categories. Among t

Algebra ->  Probability-and-statistics -> SOLUTION: A random sample of 250 students entering the university included 120 females, of whom 20 belonged to a minority group, 65 had averages over 80%, and 10 fit both categories. Among t      Log On


   



Question 856507: A random sample of 250 students entering the university included 120 females, of whom 20 belonged to a minority group, 65 had averages over 80%, and 10 fit both categories. Among the 250 students, a total of 105 people in the sample had averages over 80%, and a total of 40 belonged to the minority group. Fifteen males in the minority group had averages over 80%
i) Given a person was a male from the minority group, what is the probability he had an average over 80%? ii) What is the probability that a person selected at random was male, did not come from the minority group, and had an average less than 80%?

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if i got the counts right, these are the numbers;

                               female      male     total

students                         120        130       250
black                             20         20        40
white                            100        110       210


greater than 80%                  65         40        105
black                             10         15         25
white                             55         25         80


less than or equal to 80%         55         90        145
black                             10          5         15
white                             45         85        130




answers to the questions:

i) Given a person was a male from the minority group, what is the probability he had an average over 80%?

20 males from a minoty group and 15 of them have 80% or higher so the probability is 15/20 = 3/4 = 75%

ii) What is the probability that a person selected at random was male, did not come from the minority group, and had an average less than 80%?

this would be a white male with an average less than 80%.
from the table, there are 85 of them.
the probability is therefore 85/250 = 34%