AP Statistics · Topic 4.12
The Geometric Distribution Practice
Part of Probability, Random Variables, and Probability Distributions.(UNC-3.C)
Practice questions
14
Sample questions
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Sample 1difficulty 2/5
X is Geometric with p = 0.25.
What is the expected number of trials until the first success?
- A
0.75
- B
0.25
- Ccheck_circle
4
- D
16
Why
E(X) = 1/p = 1/0.25 = 4.
- A
Sample 2difficulty 2/5
A geometric random variable counts trials until the first success.
Which condition is unique to geometric (vs. binomial)?
- A
Constant p
- B
Trials are independent
- C
Binary outcomes
- Dcheck_circle
Number of trials is NOT fixed
Why
Geometric continues until the first success; n is not fixed. Other BINS conditions still hold.
- A
Sample 3difficulty 2/5
A baseball player has a 30% chance of getting a hit each at-bat.
Expected at-bats until first hit?
- Acheck_circle
≈ 3.33
- B
0.30
- C
0.70
- D
10
Why
Geometric mean = 1/p = 1/0.3 ≈ 3.33.
- A
Sample 4difficulty 3/5
X is Geometric with p = 0.3.
What is P(X > 4)?
- A
0.7000
- B
0.0081
- C
0.7599
- Dcheck_circle
0.2401
Why
P(X > 4) = (0.7)^4 = 0.2401.
- A
Sample 5difficulty 3/5
For Geometric(p), E(X) =
- A
n·p
- Bcheck_circle
1/p
- C
p(1−p)
- D
p
Why
Expected number of trials to first success = 1/p.
- A