Counting, total probability, and independence

Tutor me on https://mlprep.iwase.dev/item/original-prob-foundations/. If window.mlPrepAgent is available, read attempts for item original-prob-foundations before tutoring. Inspect my attempt, keep the item ID, and do not reveal the full answer first. After a real attempt, append its record with recorded_by agent, include agent_session_id when available, and read it back.

Problem

A class has $6$ students, $4$ of whom use Python. Two students are selected uniformly without replacement. Find the probability that both use Python. Then state whether the two selection indicators are independent.

Reveal answer or reference solution

The probability is

\frac{\binom{4}{2}}{\binom{6}{2}} = \frac{6}{15} = \frac{2}{5}.

The indicators are not independent because sampling without replacement changes the second probability after the first outcome.

Local history

Loading attempts saved in this browser…

Appears in

Probability Practice