a hat? Interpret this probability. Select the correct choice below and fill in the answer boxes within your choice. (Type an integer or decimal rounded to the nearest thousandth as needed) A. The probability is approximately 0.113 So, for every 1000 home runs caught by fans, we expect about 113 to have been caught in a hat B. The probabiity is $$ \square $$ So, for every 1000 home runs caught by fans, we expect exactly $$ \square $$ to have been caught in a hat. (d) Or the 284 dropped batts, it was determined that 214 were barehanded aftempts, 57 were dropped with a glove, and 13 were dropped with a failed hat atter dropped bal was a falled hat attempt? Interpret this probability Select the corred choice below and fill in the ancwor boves withen your choice (Type an integer or decimal rounded to the nearest thousandth as needed.) A. The probability is $$ \square $$ So, for every 1000 home runs dropped when a fan made an aftempt to catch the ball, we expect exactly $$ \square $$ fo have been a failed B. The probability is approximately $$ \square $$ So, for every 1000 home runs dropped when a fan made an attempt to catch the Batt, we expect about $$ \square $$ to have b

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To interpret the probabilities given in the problem, we need to calculate the probabilities based on the provided data.

### Part 1: Home Runs Caught in a Hat

1. **Known Conditions**:
   - Total home runs caught by fans: 1000
   - Expected home runs caught in a hat: 113

2. **Probability Calculation**:
   The probability of catching a home run in a hat can be calculated as:
   $$
   P(\text{hat}) = \frac{\text{Number of home runs caught in a hat}}{\text{Total home runs caught}} = \frac{113}{1000}
   $$

3. **Interpretation**:
   - A. The probability is approximately $$0.113$$. So, for every 1000 home runs caught by fans, we expect about 113 to have been caught in a hat.

### Part 2: Failed Hat Attempts

1. **Known Conditions**:
   - Total dropped bats: 284
   - Barehanded attempts: 214
   - Dropped with a glove: 57
   - Dropped with a failed hat: 13

2. **Probability Calculation**:
   The probability of a failed hat attempt can be calculated as:
   $$
   P(\text{failed hat}) = \frac{\text{Number of failed hat attempts}}{\text{Total dropped bats}} = \frac{13}{284}
   $$

3. **Calculating the Probability**:
   Let's calculate this probability and round it to the nearest thousandth.

Now, I will perform the calculation for the probability of a failed hat attempt.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{13}{284}$$
The probability of a failed hat attempt is approximately $$0.046$$ when rounded to the nearest thousandth.

### Interpretation:
- B. The probability is approximately $$0.046$$. So, for every 1000 home runs dropped when a fan made an attempt to catch the ball, we expect about $$46$$ to have been a failed hat attempt.

### Summary of Answers:
1. For home runs caught in a hat:
   - A. The probability is approximately $$0.113$$. So, for every 1000 home runs caught by fans, we expect about $$113$$ to have been caught in a hat.

2. For failed hat attempts:
   - B. The probability is approximately $$0.046$$. So, for every 1000 home runs dropped when a fan made an attempt to catch the ball, we expect about $$46$$ to have been a failed hat attempt.
For every 1000 home runs caught by fans, about 113 were caught in a hat. For every 1000 home runs dropped when a fan attempted to catch the ball, about 46 were failed hat attempts.

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