Distinct toy cards among six kids' meals

Question

Six people each buy a meal that includes one of four collectible cards, each equally likely and independent. How many distinct cards should the group expect to end up with?

Short answer

$4\left(1-(3/4)^6\right)\approx3.29$ . Use one indicator per card: a given card is absent from all six meals with probability $(3/4)^6$ , and linearity gives the result.

Adapted from OpenQuant; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Counting and Combinatorics
Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

Start with a free lesson: Probability Fundamentals is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free