AP Statistics · Topic 4.6
Independent Events and Unions of Events Practice
Part of Probability, Random Variables, and Probability Distributions.(VAR-4.D)
Practice questions
10
Sample questions
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Sample 1difficulty 3/5
Two independent events have P(A) = 0.7, P(B) = 0.6.
What is P(A or B)?
- A
0.30
- Bcheck_circle
0.88
- C
1.30
- D
0.42
Why
P(A and B) = 0.42. P(A or B) = 0.7 + 0.6 - 0.42 = 0.88.
- A
Sample 2difficulty 3/5
A bag contains 5 red and 3 blue marbles. Two are drawn without replacement.
What is the probability both are red?
- Acheck_circle
20/56
- B
10/28
- C
5/8
- D
25/64
Why
P(R1) * P(R2|R1) = (5/8) * (4/7) = 20/56.
- A
Sample 3difficulty 3/5
A two-way table of 100 outcomes is shown.
Are events A and B independent?
- A
No; P(A|B) ≠ P(A)
- B
Cannot determine
- Ccheck_circle
Yes; P(A|B) = P(A) = 0.40
- D
Yes; they are mutually exclusive
Why
P(A) = 40/100 = 0.40. P(A|B) = 12/30 = 0.40. Since equal, A and B are independent.
- A
Sample 4difficulty 3/5
Three independent events each have probability 0.4.
What is the probability all three occur?
- A
0.160
- B
1.200
- C
0.400
- Dcheck_circle
0.064
Why
Independence: 0.4^3 = 0.064.
- A
Sample 5difficulty 3/5
P(A) = 0.5, P(B) = 0.4, A and B independent. P(A and B) =
- A
0.90
- Bcheck_circle
0.20
- C
0.50
- D
0.10
Why
0.5 × 0.4 = 0.20.
- A