Probability of Failed Hat Attempts in Dropped Balls

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Question:

​(d) Of the 263 dropped​ balls, it was determined that 205 were barehanded​ attempts, 55 were dropped with a​ glove, and 3 were dropped with a failed hat attempt. What is the probability a randomly selected dropped ball was a failed hat​ attempt? 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    enter your response here. ​So, for every 1000 home runs dropped when a fan made an attempt to catch the​ ball, we expect about    enter your response here to have been a failed hat attempt. B. The probability is    enter your response here. ​So, for every 1000 home runs dropped when a fan made an attempt to catch the​ ball, we expect exactly    enter your response here to have been a failed hat attempt.

Answer:

To find the probability that a randomly selected dropped ball was a failed hat attempt, we divide the number of failed hat attempts by the total number of dropped balls.

The number of failed hat attempts is 3, and the total number of dropped balls is 263.

The probability is calculated as follows:

[ \text{Probability} = \frac{\text{Number of failed hat attempts}}{\text{Total number of dropped balls}} = \frac{3}{263} \approx 0.011 ]

This probability can be interpreted as follows: For every 1000 home runs dropped when a fan made an attempt to catch the ball, we expect about 11 to have been a failed hat attempt.

Therefore, the correct choice is:

A. The probability is approximately 0.011. So, for every 1000 home runs dropped when a fan made an attempt to catch the ball, we expect about 11 to have been a failed hat attempt.