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8. A basketball player has a free throw percentage of 80%. He was fouled while attempting a three-point shot and will be shooting 3 free throws. Make a probability distribution for the number of shots he makes. a. List all possible outcomes: b. List all events; in this case, what are the possible numbers of shots made? c. Find the probability of each event and display the probabilities in the table: Event Probability of Event 1/4 A players. How much will the casino expect to make. Total

8. A basketball player has a free throw percentage of 80%. He was fouled while attempting a three-point shot and will be shooting 3 free throws. Make a probability distribution for the number of shots he makes. a. List all possible outcomes: b. List all events; in this case, what are the possible numbers of shots made? c. Find the probability of each event and display the probabilities in the table: Event Probability of Event 1/4 A players. How much will the casino expect to make. Total

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Problem 8: Probability Distribution of Free Throws** A basketball player has a free throw shooting percentage of 80%. He was fouled while attempting a three-point shot and will be shooting 3 free throws. Make a probability distribution for the number of shots he makes. a. **List all possible outcomes:** - Possible outcomes for each shot could be: Made (M) or Missed (X). - Combined outcomes for 3 shots could be: - MMM - MMX - MXM - MXX - XMM - XMX - XXM - XXX b. **List all events; in this case, what are the possible numbers of shots made?** - Possible numbers of successful shots: 0, 1, 2, or 3. c. **Find the probability of each event and display the probabilities in the table:** | Event | Probability of Event | |-------|----------------------| | Makes 0 shots | P(Made=0) | | Makes 1 shot | P(Made=1) | | Makes 2 shots | P(Made=2) | | Makes 3 shots | P(Made=3) | | **Total** | **1.0** | **Note:** The probabilities for each entry in the table depend on calculating the number of ways each event can occur multiplied by the probability of each outcome, based on the 80% success rate per shot and 20% failure rate.
Transcribed Image Text:**Problem 8: Probability Distribution of Free Throws** A basketball player has a free throw shooting percentage of 80%. He was fouled while attempting a three-point shot and will be shooting 3 free throws. Make a probability distribution for the number of shots he makes. a. **List all possible outcomes:** - Possible outcomes for each shot could be: Made (M) or Missed (X). - Combined outcomes for 3 shots could be: - MMM - MMX - MXM - MXX - XMM - XMX - XXM - XXX b. **List all events; in this case, what are the possible numbers of shots made?** - Possible numbers of successful shots: 0, 1, 2, or 3. c. **Find the probability of each event and display the probabilities in the table:** | Event | Probability of Event | |-------|----------------------| | Makes 0 shots | P(Made=0) | | Makes 1 shot | P(Made=1) | | Makes 2 shots | P(Made=2) | | Makes 3 shots | P(Made=3) | | **Total** | **1.0** | **Note:** The probabilities for each entry in the table depend on calculating the number of ways each event can occur multiplied by the probability of each outcome, based on the 80% success rate per shot and 20% failure rate.
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