The outcome of any o 2-point shots, and 75 probability that he ma
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![### Probability Calculation in Basketball Shooting
In basketball, there are three different types of shots each with distinct point values:
- 3-point shots
- 2-point shots
- 1-point shots (free throws)
Each shot can result in either a successful make or a miss.
**Scenario:** LeBron James' shooting probabilities are given as follows:
- He makes 35% of his 3-point shots.
- He makes 55% of his 2-point shots.
- He makes 75% of his free throws.
**Problem Statement:**
If LeBron shoots one 3-pointer, then one 2-pointer, and finishes with a free throw, what is the probability he makes all three shots?
**Answer Options:**
A. 1.65%
B. 7.31%
C. 12.5%
D. 14.43%
**Solution:**
To find the probability that LeBron makes all three shots, you multiply the probabilities of making each individual shot. The calculations are as follows:
\[ P(\text{All 3 shots}) = P(\text{3-pointer}) \times P(\text{2-pointer}) \times P(\text{free throw}) \]
Given probabilities:
- \( P(\text{3-pointer}) = 0.35 \)
- \( P(\text{2-pointer}) = 0.55 \)
- \( P(\text{free throw}) = 0.75 \)
\[ P(\text{All 3 shots}) = 0.35 \times 0.55 \times 0.75 \]
**Step-by-step Calculation:**
1. Multiply the probability of making the 3-pointer with the probability of making the 2-pointer:
\[ 0.35 \times 0.55 = 0.1925 \]
2. Multiply the result by the probability of making the free throw:
\[ 0.1925 \times 0.75 = 0.144375 \]
So, the probability that LeBron makes all three shots is 0.144375, which is approximately 14.44%.
Hence, the correct answer is:
**D. 14.43%**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e4a772a-c051-4e28-ae1b-1a6b5a7947cd%2F9c8a5d63-43b8-4083-9efa-301b7adfa0fc%2Fgldvxqj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Calculation in Basketball Shooting
In basketball, there are three different types of shots each with distinct point values:
- 3-point shots
- 2-point shots
- 1-point shots (free throws)
Each shot can result in either a successful make or a miss.
**Scenario:** LeBron James' shooting probabilities are given as follows:
- He makes 35% of his 3-point shots.
- He makes 55% of his 2-point shots.
- He makes 75% of his free throws.
**Problem Statement:**
If LeBron shoots one 3-pointer, then one 2-pointer, and finishes with a free throw, what is the probability he makes all three shots?
**Answer Options:**
A. 1.65%
B. 7.31%
C. 12.5%
D. 14.43%
**Solution:**
To find the probability that LeBron makes all three shots, you multiply the probabilities of making each individual shot. The calculations are as follows:
\[ P(\text{All 3 shots}) = P(\text{3-pointer}) \times P(\text{2-pointer}) \times P(\text{free throw}) \]
Given probabilities:
- \( P(\text{3-pointer}) = 0.35 \)
- \( P(\text{2-pointer}) = 0.55 \)
- \( P(\text{free throw}) = 0.75 \)
\[ P(\text{All 3 shots}) = 0.35 \times 0.55 \times 0.75 \]
**Step-by-step Calculation:**
1. Multiply the probability of making the 3-pointer with the probability of making the 2-pointer:
\[ 0.35 \times 0.55 = 0.1925 \]
2. Multiply the result by the probability of making the free throw:
\[ 0.1925 \times 0.75 = 0.144375 \]
So, the probability that LeBron makes all three shots is 0.144375, which is approximately 14.44%.
Hence, the correct answer is:
**D. 14.43%**
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