Last-second shot choice when trailing by two

Question

Your basketball team is two points behind with time for one final shot. A three-point attempt goes in $40\%$ of the time and wins the game. A two-point attempt goes in $70\%$ of the time but only ties the game, after which overtime is a coin flip. Which shot gives the better chance of winning?

Short answer

The three-pointer. It wins with probability $0.40$ , whereas the two-pointer wins with probability $0.70\times0.50=0.35$ .

Adapted from Crack, Heard on the Street, Q4.17, p.40; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Expectation, Mean, and Variance
Conditional Expectation and Variance Revisited
Sample Spaces, Events, and the Probability Axioms

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