A study of graduates average grades and degrees showed the following results: B.S. Degrees, 15 graduates averaged Grade A, 8 graduates averaged Grade B, and 5 graduates averaged grade C. Graduates who had a B.A. Degree, 8 averaged grade A, 12 averaged grade B, and 7 averaged Grade C. If a graduate is selected at random, find this probability:
1. The graduate has a B.S. Degree, given that he or she has an A average
2. Given that the graduate has a B.A. degree, the graduate has a C average.
1. 15/total number of BS degrees = ?
2. 7/total number of BA degrees = ?
To find the probabilities, we need to use conditional probability. Let's solve each question separately:
1. The graduate has a B.S. Degree, given that he or she has an A average.
To find this probability, we need to determine the number of B.S. graduates who have an A average and divide it by the total number of graduates who have an A average.
The number of B.S. graduates with an A average is 15.
The total number of graduates with an A average is 15 + 8 + 8 = 31 (15 B.S. + 8 B.A. + 8 B.S.).
Therefore, the probability is: 15/31 ≈ 0.4839 or approximately 48.39%.
2. Given that the graduate has a B.A. degree, the graduate has a C average.
To find this probability, we need to determine the number of B.A. graduates who have a C average and divide it by the total number of graduates who have a B.A. degree.
The number of B.A. graduates with a C average is 7.
The total number of graduates with a B.A. degree is 8 + 12 + 7 = 27 (8 B.S. + 12 B.A. + 7 B.S.).
Therefore, the probability is: 7/27 ≈ 0.2593 or approximately 25.93%.
To find the probabilities, we need to use conditional probability, which is the probability of an event A given that event B has already occurred. In this case, we need to find the probability of having a B.S. degree given an A average and the probability of having a C average given a B.A. degree.
1. The probability of a graduate having a B.S. degree, given an A average:
We know that there are 15 graduates with B.S. degrees who averaged an A grade. To find the probability, we need to divide the number of graduates with B.S. degrees and A grades by the total number of graduates who averaged an A grade.
Total number of graduates with an A average = Number of graduates with B.S. degrees and A average + Number of graduates with B.A. degrees and A average
Total number of graduates with an A average = 15 + 8 = 23
P(B.S. degree | A average) = Number of graduates with B.S. degrees and A average / Total number of graduates with an A average
P(B.S. degree | A average) = 15 / 23
So, the probability of a graduate having a B.S. degree, given an A average, is 15/23.
2. The probability of a graduate having a C average, given a B.A. degree:
We know that there are 7 graduates with B.A. degrees who averaged a C grade. To find the probability, we need to divide the number of graduates with B.A. degrees and C grades by the total number of graduates who have B.A. degrees.
Total number of graduates with B.A. degrees = Number of graduates with B.A. degrees and A average + Number of graduates with B.A. degrees and B average + Number of graduates with B.A. degrees and C average
Total number of graduates with B.A. degrees = 8 + 12 + 7 = 27
P(C average | B.A. degree) = Number of graduates with B.A. degrees and C average / Total number of graduates with B.A. degrees
P(C average | B.A. degree) = 7 / 27
So, the probability of a graduate having a C average, given a B.A. degree, is 7/27.