Let's determine the overall success rate, or probability, of Kristen making a free throw based on her performance in the previous three games.
1. Step 1: Find the total number of successful free throws.
- In the first game, Kristen made 4 successful free throws.
- In the second game, Kristen made 5 successful free throws.
- In the third game, Kristen made 5 successful free throws.
Adding these together gives:
[tex]\[
4 + 5 + 5 = 14
\][/tex]
2. Step 2: Find the total number of attempted free throws.
- In the first game, Kristen attempted 5 free throws.
- In the second game, Kristen attempted 5 free throws.
- In the third game, Kristen attempted 7 free throws.
Adding these together gives:
[tex]\[
5 + 5 + 7 = 17
\][/tex]
3. Step 3: Calculate the overall probability of making a free throw.
The probability of making a free throw is the ratio of successful free throws to attempted free throws:
[tex]\[
\text{Overall probability} = \frac{\text{successful free throws}}{\text{attempted free throws}} = \frac{14}{17}
\][/tex]
The overall probability of Kristen making a free throw is:
[tex]\[
\frac{14}{17} \approx 0.8235
\][/tex]
4. Step 4: Compare the calculated probability to the given options and choose the closest one.
- Option 1: [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex]
- Option 2: [tex]\( \frac{3}{4} = 0.75 \)[/tex]
- Option 3: [tex]\( \frac{7}{10} = 0.7 \)[/tex]
None of the given options, [tex]\( \frac{2}{3} \)[/tex], [tex]\( \frac{3}{4} \)[/tex], or [tex]\( \frac{7}{10} \)[/tex], closely match the actual calculated probability of [tex]\( 0.8235 \)[/tex]. Therefore, none of the options provided are correct based on the given data.
