Suppose that for a recent admissions class, an Ivy League college received 2,861 applications for early admission. Of this group, it admitted 1,037 students early, rejected 856 outright, and deferred 968 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2,373. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.
(a)
Use the data to estimate 
P(E), P(R), and P(D).
(b)
Are events E and D mutually exclusive?
Find 
P(E ∩ D).
(c)
For the 2,373 students who were admitted, what is the probability that a randomly selected student was accepted during early admission?
(d)
Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?
Step 1
(a)
Use the data to estimate P(E), P(R), and P(D).
To organize the given data and calculations, it can be helpful to use Excel. Create an Excel spreadsheet using the following format. It is given that 2,861 student applications were received for early admission. Of these, 1,037 students were admitted early (event E), 856 were rejected (event R), and 968 were deferred (event D). Place these values in the table.
A	B	C	D
1	Applications for early admission	
2	Outcome	Event	Frequency	Probability
3	Admitted	E	1037 
Correct: Your answer is correct.
 seenKey 1,037	
4	Rejected	R	856 
Correct: Your answer is correct.
 seenKey 856	
5	Deferred	D	968 
Correct: Your answer is correct.
 seenKey 968	
6	Total		2,861	
Recall that the probability of an event is found by dividing the number of times an event occurs by the number of all possible outcomes. That is, the probability for each outcome will be found by dividing the outcome frequency by the total number of applications.
In cell D3, the probability that a student is admitted early is found by dividing the frequency of that outcome by the total number of applicants. Since this formula will be copied into other cells, the absolute cell reference should be used for the total value. Thus, the formula to calculate the probability of event E is =C3/$C$6 
Correct: Your answer is correct.
 seenKey =C3/$C$6 .
Step 2
We determined the probability for each outcome will be found by dividing the outcome frequency by the total number of applications. In the Excel spreadsheet, this can be accomplished by entering the formula =C3/$C$6 in cell D3. Copy this formula to cells D4 and D5 to find the requested probabilities, rounding each to four decimal places.
A	B	C	D
1	Applications for early admission	
2	Outcome	Event	Frequency	Probability
3	Admitted	E	1,037	P(E) = 0.3625 
Correct: Your answer is correct.
 seenKey 0.3625
4	Rejected	R	856	P(R) = 0.2992 
Correct: Your answer is correct.
 seenKey 0.2992
5	Deferred	D	968	P(D) = 0.3383 
Correct: Your answer is correct.
 seenKey 0.3383
6	Total		2,861	
Step 3
(b)
Are events E and D mutually exclusive? Find 
P(E ∩ D).
Events are mutually exclusive when they have no common outcomes. That is, their intersection contains no sample points.
Recall that event E is the event a student who applies for early admission is admitted early. Event D is the event a student who applies for early admission is deferred to the regular admissions pool. Those students who are deferred to the regular admissions pool have not 
Correct: Your answer is correct.
 seenKey have not been admitted early. Thus, events E and D are 
Correct: Your answer is correct.
 seenKey are mutually exclusive.
Step 4
Since events E and D are mutually exclusive there are no common points in their intersection. Thus, there are 
 
Incorrect: Your answer is incorrect.
 students who were both admitted early and deferred to the regular admissions pool so 
P(E ∩ D) = 
0.12263
 
Incorrect: Your answer is incorrect.
 .