
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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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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