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### Course: Statistics and probability>Unit 7

Lesson 2: Probability using sample spaces

# Subsets of sample spaces

You might need: Calculator

## Problem

Anna and Charles have a bag that contains $1$ black marble and $1$ white marble. They are playing a game where they randomly select a marble out of the bag three times, with replacement.
Anna thinks that the probability of getting a black marble on the first selection and a black marble on the third selection is greater than the probability of getting a black marble on the first selection and a white marble on the third selection. Charles disagrees. He thinks that the two probabilities are equal.
The sample space of possible outcomes is listed below. B represents a black marble, and W represents a white marble.
Who is correct, Anna or Charles?