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Football Field Goal Probabilities: A Multi-Player Analysis
Chapter 1, Problem 7(choose chapter or problem)
Each of three football players will attempt to kick a field goal from the 25-yard line. Let \(A_{i}\) denote the event that the field goal is made by player \(i, i=1,2,3 \text {. }\) Assume that \(A_{1}, A_{2}, A_{3}\) are mutually independent and that \(P\left(A_{1}\right)=0.5, P\left(A_{2}\right)=0.7, P\left(A_{3}\right)=0.6\)
(a) Compute the probability that exactly one player is successful.
(b) Compute the probability that exactly two players make a field goal (i.e., one misses).
Questions & Answers
QUESTION:
Each of three football players will attempt to kick a field goal from the 25-yard line. Let \(A_{i}\) denote the event that the field goal is made by player \(i, i=1,2,3 \text {. }\) Assume that \(A_{1}, A_{2}, A_{3}\) are mutually independent and that \(P\left(A_{1}\right)=0.5, P\left(A_{2}\right)=0.7, P\left(A_{3}\right)=0.6\)
(a) Compute the probability that exactly one player is successful.
(b) Compute the probability that exactly two players make a field goal (i.e., one misses).
ANSWER:Step 1 of 3
(a) We have three football players, A1, A2, and A3, each attempting a field goal. Let's examine the probability of each of them making or missing the goal. The success rates are 50% for A1, 70% for A2, and 60% for A3.
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Football Field Goal Probabilities: A Multi-Player Analysis
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Discover the art of calculating probabilities in football. Using three players' success rates, we determine the odds of different goal outcomes. Understand independent and mutually exclusive events in a real-world scenario.