Homework SourseYou are in your senior year and you apply to two graduate sc
You are in your senior year, and you apply to two graduate schools, say school X and school Y. Each school may:
F : Admit you, and offer you a prestigious graduate school Fellowship; or
T : Admit you and offer you a highly sought-after Teaching or research assistantship; or
A : Offer you addmission, but without any kind of financial aid; or
R : Reject your application.
The sample space for this experimen is the set of 16 ordered pairs (X, Y) with X belonging to { R, A, T, F}, and Y belonging to { R, A, T, F}. The probability of each outcome is given in table below, where the x-axis is school X and y-axis is school Y.
a. Find the probabilty that you are admitted in school Y, but not in school X.
b. Find the probability that you are admitted to school X, but not in school Y.
c. Find the probability that you are offerered financial aid in school Y but not in school X.
d.Find the probability that you are offered financial aid in both the schools.
e. Find the probability that you are offered financial aid in school Y.
f. Are the two events X belonging to {T, F} and Y belonging to {T,F} independent?
| F | 0 | 0 | 1/8 | 1/8 |
| T | 1/32 | 1/16 | 1/8 | 1/32 |
| A | 1/16 | 1/4 | 1/32 | 0 |
| R | 1/8 | 1/32 | 0 | 0 |
| P(X,Y) | R | A | T | F |
Solution
