AP Statistics · Topic 4.5
Conditional Probability Practice
Part of Probability, Random Variables, and Probability Distributions.(VAR-4.C)
Practice questions
17
Sample questions
5 of 17 — sign in to practice the rest with adaptive difficulty and mastery tracking.
Sample 1difficulty 3/5
A tree diagram shows P(A) = 0.6, P(B|A) = 0.7, P(B|A^c) = 0.2.
What is P(A and B)?
- A
0.70
- B
0.60
- C
0.30
- Dcheck_circle
0.42
Why
P(A and B) = P(A) * P(B|A) = 0.6 * 0.7 = 0.42.
- A
Sample 2difficulty 3/5
A two-way table classifies 100 items by row (X/Y) and column (A/B).
What is P(A | Y)?
- A
35/50
- B
15/40
- Ccheck_circle
35/60
- D
35/100
Why
Row Y total = 35 + 25 = 60. P(A | Y) = 35/60.
- A
Sample 3difficulty 3/5
Definition of conditional probability.
P(A | B) equals:
- A
P(A) * P(B)
- Bcheck_circle
P(A and B) / P(B)
- C
P(A) / P(B)
- D
P(A) + P(B)
Why
By definition, P(A|B) = P(A and B)/P(B).
- A
Sample 4difficulty 3/5
A bag is chosen at random (50/50). Bag 1: P(Red) = 0.6. Bag 2: P(Red) = 0.3.
What is P(Red)?
- A
0.60
- Bcheck_circle
0.45
- C
0.90
- D
0.30
Why
P(Red) = 0.5(0.6) + 0.5(0.3) = 0.30 + 0.15 = 0.45.
- A
Sample 5difficulty 3/5
P(A and B) =
- Acheck_circle
P(A) · P(B|A)
- B
P(A) + P(B)
- C
P(B) − P(A)
- D
P(A) · P(B)
Why
Holds always (independence is the special case where P(B|A) = P(B)).
- A