University of Toronto Mississauga
Probability and Statistics I
Term Test #1
Aids Allowed: nongraphing calculator without a text keypad
Printed Name: __________________________________________________
Student Number: ________________________________________________
TA, Muz, Charles or LingLing:_______________________________________
1. (3 marks) Events A and B satisfy P(A) = 0.8 and P(B) = 0.4. What is the smallest possible
value for P(AB)? You must justify your answer; there are no marks if you simply write a
Page 1 of 4 2. (10 marks) The random variable X has probability mass function
x 1 0 1 2
p(x) 0.2 0.3 0.4 0.1
Answer each of the following questions. Put your answers in the chart below. Only answers
in the chart will be marked.
a. Find P(X = 1)
b. Find P (X ≤ 1)
c. Find E(X)
d. Find E(X ) 2
3. (4 marks) Spike is not bright. The probability he passes chemistry is 0.35, the probability
he passes calculus is 0.40 and the probability he passes both is 0.12.
a. Are the events “Spike passes chemistry” and “Spike passes calculus” independent?
Justify your answer.
b. What is the probability he fails both courses?