Question

Kristen made 4 out of 5 free throws in her first basketball game, 5 out of 8 free throws in her second game, and 5 out of 7 free throws in her third game what is the experimental probability of Kristen making her first free throw in her fourth game?

Answer 1

To calculate the experimental probability of Kristen making her first free throw in her fourth game, we need to look at her total successful free throws and total attempted free throws across the first three games in order to estimate her likelihood of making the first free throw in the fourth game.

1. **Calculating Total Successful Free Throws**:
- In the first game: 4 successful out of 5 attempts
- In the second game: 5 successful out of 8 attempts
- In the third game: 5 successful out of 7 attempts

Total successful free throws:
\[
4 + 5 + 5 = 14
\]

2. **Calculating Total Free Throw Attempts**:
- First game: 5 attempts
- Second game: 8 attempts
- Third game: 7 attempts

Total attempts:
\[
5 + 8 + 7 = 20
\]

3. **Calculating the Experimental Probability**:
The experimental probability \( P \) of making a free throw is given by the ratio of successful free throws to total attempts:
\[
P(\text{making a free throw}) = \frac{\text{Total Successful Free Throws}}{\text{Total Free Throw Attempts}} = \frac{14}{20}
\]
Simplifying this fraction:
\[
P = \frac{14 \div 2}{20 \div 2} = \frac{7}{10}
\]

Thus, the experimental probability of Kristen making her first free throw in her fourth game is \( \frac{7}{10} \) or 0.7 (70%).