Student Admissions Exercises 69–84 are based on the following table, which shows the profile, by the math section of the SAT Reasoning Test, of admitted students at UCLA for the Fall 2014 semester:^{44}
SAT Reasoning Test—Math Section
700–800 | 600–699 | 500–599 | 400–499 | 200–399 | Total | |
Admitted | 8,398 | 3,517 | 1,410 | 358 | 9 | 13,692 |
Not Admitted | 16,599 | 18,363 | 13,119 | 6,714 | 1,652 | 56,447 |
Total Applicants | 24,997 | 21,880 | 14,529 | 7,072 | 1,661 | 70,139 |
Determine the probabilities of the following events. (Round your answers to the nearest .01.) [HinT: Example 6.]
An applicant had a Math SAT of 700 or above or was admitted.
To calculate: The probability that an applicant had a Math SAT of 700 or above or was admitted from table of the math section of the SAT reasoning test of students admitted at UCLA for the fall semester 2014.
SAT Reasoning Test-Math Section
700-800 | 600-699 | 500-599 | 400-499 | 200-399 | Total | |
Admitted | 8,398 | 3,517 | 1,410 | 358 | 9 | 13,692 |
Not Admitted | 16,599 | 18,363 | 13,119 | 6,714 | 1,652 | 56,447 |
Total Applicants | 24,997 | 21,880 | 14,529 | 7,072 | 1,661 | 70,139 |
Given Information:
The following table shows the profile, by the math section of the SAT reasoning test of students admitted at UCLA for the fall semester 2014.
SAT Reasoning Test-Math Section
700-800 | 600-699 | 500-599 | 400-499 | 200-399 | Total | |
Admitted | 8,398 | 3,517 | 1,410 | 358 | 9 | 13,692 |
Not Admitted | 16,599 | 18,363 | 13,119 | 6,714 | 1,652 | 56,447 |
Total Applicants | 24,997 | 21,880 | 14,529 | 7,072 | 1,661 | 70,139 |
Formula used:
The probability of an event E, for sample space S is
If A and B are any two events, then the probability of union of the sets is
Calculation:
Consider the event that an applicant had a Math SAT of 700 or above to be A. Consider the event that an applicant was admitted to be B.
Consider the provided table,
SAT Reasoning Test-Math Section
700-800 | 600-699 | 500-599 | 400-499 | 200-399 | Total | |
Admitted | 8,398 | 3,517 | 1,410 | 358 | 9 | 13,692 |
Not Admitted | 16,599 | 18,363 | 13,119 | 6,714 | 1,652 | 56,447 |
Total Applicants | 24,997 | 21,880 | 14,529 | 7,072 | 1,661 | 70,139 |
From the table, the total number of applicants is 70,139. The total number of applicants who had a Math SAT of 700 or above is 24,997. The total number of applicants that were admitted is 13,692.
The total number of applicants who had Math SAT in the range 500-599 and were admitted is 1,410.
The probability that an applicant had a Math SAT of 700 or above and was admitted is found by substituting 24997 for
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