The ball is even-numbered, is it a multiple of four?

Question

A jar holds ten balls numbered 1 through 10. You draw one at random without looking, and a friend tells you the number is even. Given that, what is the probability the number is a multiple of four?

Accepted Answer

The even numbers from 1 to 10 are: \{2,\ 4,\ 6,\ 8,\ 10\}, which is five equally likely outcomes. Among them, the multiples of four are 4 and 8, so two qualify: P(	ext{multiple of }4 \mid 	ext{even}) = \frac{2}{5} = 0.4. The clue "even" cuts the pool from ten balls to five, and you simply count how many of those five hit the target. Takeaway. Conditional probability is counting inside the restricted set: favorable outcomes over the total outcomes that satisfy the clue.

The ball is even-numbered, is it a multiple of four?

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