Description

1 Venn Diagram
(a) Suppose we choose a student uniformly at random. Let C be the event that the student belongs to a club and P the event that the student works part time. Draw a picture of the sample space Ω and the events C and P.
(b) What is the probability that the student belongs to a club?
(c) What is the probability that the student works part time?
(d) What is the probability that the student belongs to a club AND works part time?
(e) What is the probability that the student belongs to a club OR works part time?
2 Flippin’ Coins
Suppose we have an unbiased coin, with outcomes H and T, with probability of heads P[H] = 1/2 and probability of tails also P[T] = 1/2. Suppose we perform an experiment in which we toss the coin 3 times. An outcome of this experiment is (X1,X2,X3), where Xi ∈{H,T}.
(a) What is the sample space for our experiment?
(b) Which of the following are examples of events? Select all that apply.
• {(H,H,T),(H,H),(T)}
• {(T,H,H),(H,T,H),(H,H,T),(H,H,H)}
• {(T,T,T)}
• {(T,T,T),(H,H,H)}
• {(T,H,T),(H,H,T)}
(c) What is the complement of the event {(H,H,H),(H,H,T),(H,T,H),(H,T,T),(T,T,T)}?
(d) Let A be the event that our outcome has 0 heads. Let B be the event that our outcome has exactly 2 heads. What is A∪B?
(e) What is the probability of the outcome (H,H,T)?
(f) What is the probability of the event that our outcome has exactly two heads?
(g) What is the probability of the event that our outcome has at least one head?
3 Counting & Probability
Consider the equation x1 +x2 +x3 +x4 +x5 +x6 = 70, where each xi is a non-negative integer. We choose one of these solutions uniformly at random.
(a) What is the size of the sample space?
(b) What is the probability that both x1 ≥ 30 and x2 ≥ 30?
(c) What it the probability that either x1 ≥ 30 or x2 ≥ 30?