Question

mason practiced basketball free throws and kept track of the results in the table. he says the experimental probability of making a free throw is \\(\frac{2}{3}\\). what is mason’s error? \
table: free throws made: 12, free throws missed: 18 \
options: \

• mason compared the number of free throws missed to the total number of free throws attempted. \
• mason compared the number of free throws made to the total number of free throws attempted. \
• mason compared the number of free throws made to the number of free throws missed. \
• mason compared the number of free throws attempted to the difference between the number made and the number missed.

Explanation:

To solve this, we first find the experimental probability of making a free throw. The number of free throws made is 12, and the number of free throws missed is 18. So the total number of free throws attempted is \(12 + 18 = 30\). The experimental probability of making a free throw is \(\frac{\text{Free Throws Made}}{\text{Total Free Throws Attempted}}=\frac{12}{30}=\frac{2}{5}\), but Mason said it was \(\frac{2}{3}\). Now we analyze each option:

Step 1: Analyze Option 1

• Explanation: Check if Mason compared missed to total.

Probability using missed to total would be \(\frac{18}{30}=\frac{3}{5}\), not \(\frac{2}{3}\). So this is not the error.

Step 2: Analyze Option 2

• Explanation: Check if Mason compared made to total.

The correct experimental probability is \(\frac{12}{30}=\frac{2}{5}\), but Mason said \(\frac{2}{3}\). Wait, no—wait, let's recalculate. Wait, total attempts are \(12 + 18 = 30\). If we mistakenly use made to missed: \(\frac{12}{18}=\frac{2}{3}\). Wait, no—wait, the options:

Wait, the options are:

1. Mason compared the number of free throws missed to the total number of free throws attempted.
2. Mason compared the number of free throws made to the total number of free throws attempted.
3. Mason compared the number of free throws made to the number of free throws missed.
4. Mason compared the number of free throws attempted to the difference between the number made and the number missed.

Wait, let's recast:

Experimental probability of making a free throw is \(\frac{\text{Made}}{\text{Total Attempted}}=\frac{12}{30}=\frac{2}{5}\). Mason said it was \(\frac{2}{3}\).

If we calculate \(\frac{\text{Made}}{\text{Missed}}=\frac{12}{18}=\frac{2}{3}\). So Mason compared the number of free throws made to the number of free throws missed (instead of made to total attempted).

So the error is that Mason compared the number of free throws made to the number of free throws missed (Option 3).

To find the experimental probability of making a free throw, we use \(\frac{\text{Free Throws Made}}{\text{Total Free Throws Attempted}}\). Here, made = 12, missed = 18, so total attempted = \(12 + 18 = 30\). The correct probability is \(\frac{12}{30}=\frac{2}{5}\). Mason’s stated probability (\(\frac{2}{3}\)) matches \(\frac{\text{Made}}{\text{Missed}}=\frac{12}{18}=\frac{2}{3}\), so he incorrectly compared made to missed (not to total attempted).

Answer:

Mason compared the number of free throws made to the number of free throws missed.