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) (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%
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