Sample Space and Subsets
Independent Events
Union and Intersection
Joint and Marginal Probability (survey table)
Conditional Probability (survey table)
100
A fair die is rolled. Write the sample space Ω.
What is Ω = {1, 2, 3, 4, 5, 6}?
100
Events A and B are independent when P(A ∩ B) equals this.
What is P(A) · P(B)?
100
In set notation, which symbol means “or” and which means “and”?
What are ∪ (or) and ∩ (and)?
100
Find P(S ∩ B).
What is 12/100 ?
100
In P(A | B), the bar means this.
What is “given that”?
200
A fair die is rolled. Let A = {2, 4, 6}. True or false: A ⊂ Ω.
What is true? (Every element of A is in Ω, and A ≠ Ω.)
200
P(A) = 0.4, P(B) = 0.5, and A and B are independent. Find P(A ∩ B).
What is 0.20?
200
A = {1, 2, 3} and B = {3, 4}. Find A ∩ B.
What is {3}?
200
Find P(S).
What is 50/100 ?
200
Find P(S | B).
What is 12/30 ?
300
A fair die is rolled. True or false: Ω ⊂ Ω.
What is false? (A set is not a proper subset of itself.)
300
A fair coin is flipped 3 times. Find P(all heads).
What is 1/8 ?
300
A = {1, 2, 3} and B = {3, 4}. Find P(A ∪ B).
What is 4/6 ?
300
Find P(not B).
What is 70/100 ?
300
Find P(B | S)
What is 12/50 ?
400
Die D has faces 5, 5, 5, 1, 1, 1, so ΩD = {1, 5}. List every proper subset of ΩD.
What are ∅, {1}, and {5}?
400
P(A) = 0.3, P(B) = 0.6, and A and B are independent. Find P(A ∪ B).
What is 0.72? (0.3 + 0.6 − 0.18)
400
P(A) = 0.5, P(B) = 0.4, and P(A ∩ B) = 0.2. Find P(A ∪ B).
What is 0.70?
400
Find P(not S ∩ B)
What is 18/100 ?
400
Find P(not S | not B).
What is 32/70 ?
500
A sample space has 3 outcomes. How many proper subsets does it have?
What is 7? (2³ = 8 subsets, minus Ω itself.)
500
A die is rolled. A = {2, 4, 6} and B = {1, 2}. Are A and B independent? Justify.
What is yes? (P(A ∩ B)) = 1/6
500
One card is drawn from a standard deck. Find P(heart ∪ face card).
What is 11/26 ?
500
Find P(S ∪ B).
What is 68/100 ?
500
P(S) = 0.50 but P(S | B) = 0.40. Are S and B independent?
What is no? (If they were independent, P(S | B) would equal P(S). Also, P(S ∩ B) = 0.12 and P(S) · P(B) = 0.15.)