Answer:
A) The probability is a measure of the likelihood than an event is going to occur. In this case we can calculate the probability of X as:
P(X) = X/N where X is the number of ways X occurs and N is the total number of events.
P(E) = E/N = 1033/2851 = 0.3623
P(R) = R/N = 854/2851 = 0.2995
P(D) = D/N = 964/2851 = 0.3381
B)
E and D are mutually exclusive because the students that were admitted early where not deffered to regular admission pool. There is no chance that there is a student that were admitted erarly and deffered at the same time, so the intersection between E and D (E∩D) is 0.
C) The number of students that were early accepted is 1033 and the total number of students accepted is 2375. The probability is going to be:
P = 1033/2375 = 0.4349
D)
In this case we can reformulate the question as: What is the probability of being accepted if you apply for early admission? This
Since 18% of the students deffered to regular admission pool 0.18 × 964 = 174 were admitted at the end.
The probability of being deffered and then accepted is going to be:
P(DA) = 174/2831 = 0.0610
The probability of ramdomly selecting a students that has been early accepted or deffered and then accepted is going to be:
P(E or DA) = 0.0610 + 0.3623 = 0.4233
This is the addition rule.
