Let's analyze Mason's claim that the experimental probability of making a free throw is [tex]\(\frac{2}{3}\)[/tex], given his recorded results.
First, we look at the numbers provided:
- Free Throws Made: [tex]\(12\)[/tex]
- Free Throws Missed: [tex]\(18\)[/tex]
### Step 1: Calculate the Total Number of Free Throws Attempted
To determine the total number of free throws Mason attempted, we add the number of free throws made to the number of free throws missed:
[tex]\[ \text{Total Free Throws Attempted} = \text{Free Throws Made} + \text{Free Throws Missed} \][/tex]
[tex]\[ \text{Total Free Throws Attempted} = 12 + 18 \][/tex]
[tex]\[ \text{Total Free Throws Attempted} = 30 \][/tex]
### Step 2: Calculate the Experimental Probability
The experimental probability of making a free throw is given by the ratio of the number of successful free throws (made) to the total number of free throws attempted:
[tex]\[ \text{Experimental Probability} = \frac{\text{Free Throws Made}}{\text{Total Free Throws Attempted}} \][/tex]
[tex]\[ \text{Experimental Probability} = \frac{12}{30} \][/tex]
[tex]\[ \text{Experimental Probability} = \frac{2}{5} \][/tex]
### Step 3: Evaluate Mason's Claim
Mason claims that the experimental probability of making a free throw is [tex]\(\frac{2}{3}\)[/tex]. However, our calculations show that the actual experimental probability, based on the data provided, is [tex]\(\frac{2}{5}\)[/tex].
### Conclusion
Mason's claim is not correct. Based on his recorded results, the experimental probability of making a free throw is [tex]\(\frac{2}{5}\)[/tex] or 0.4, not [tex]\(\frac{2}{3}\)[/tex].
