In a Free-Throw Relay, One Member of a Team of Four

question 56

Multiple Choice

In a free-throw relay, one member of a team of four shoots free-throws (a type of shot in basketball) until she makes one, then the next team member shoots until she makes one. This continues through the third and forth team members. In a competition, the first team to finish wins. The question arises whether it is better to have four average shooters or two good shooters and two not-so-good ones, if the overall shooting percentage of the teams is the same. Use a Monte Carlo simulation to help answer this question. Each number in the random numbers table below will correspond to one free throw.
One simulated team has four 50% free-throw shooters (the 50's) . The order of the shooters does not matter. The digits 0-4 will correspond to making a free throw and the digits 5-9 will correspond to missing.
The other simulated team has two 80% free-throw shooters and two 20% free-throw shooters (the 80/20's) . Let the 80% shooters be the first two of the four to shoot. For the 80% shooters, the digits 0-7 will correspond to making the free throw, and the digits 8-9 will correspond to missing. For the 20% shooters, the digits 0-1 will correspond to making the free throw and 2-9 will correspond to missing.
Work down the columns, moving to the column to the right as needed. The highlighted numbers were selected at random. Begin the 80/20's team at the 6, and begin the 50's team at the 7. Simulate one race for each team. Count the number of shots each team needs to finish.

• A) The 80's/20's needed 10, while the 50's needed 10
• B) The 80's/20's needed 8, while the 50's needed 5
• C) The 80's/20's needed 5, while the 50's needed 7
• D) The 80's/20's needed 4, while the 50's needed 8

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