Practice Geometric Distribution in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The probability distribution for the number of independent Bernoulli trials needed to get the first success, where each trial has success probability p.

How many times do you have to roll a die before you get a 6? The geometric distribution answers this kind of question. Each trial is independent, and you keep going until you succeed. Most of the time it doesn't take too long, but occasionally you have an unlucky streak—that's why the distribution has a long right tail.

Example 1

medium
A basketball player makes free throws with probability p=0.7. Find the probability they make their first free throw on exactly the 3rd attempt.

Example 2

hard
For a geometric distribution with p=0.4: (a) find P(X \leq 3), (b) find the expected number of trials until first success.

Example 3

easy
A fair coin is flipped until heads appears. What is P(\text{first heads on flip 4}), and what is the expected number of flips?

Example 4

hard
A quality inspector samples items until finding the first defective. Defect probability is p=0.05. Find P(X > 10) (probability of needing more than 10 inspections) and the expected number to inspect.
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