The Wall Street Journal regularly publishes an article entitled "The Count." In one article, The Count looked at 1000 randomly selected home runs in Major League Baseball. Complete parts (a) through (d) below. Question content area bottom Part 1 (a) Of the 1000 home runs, it was found that 75 were caught by fans. What is the probability that a randomly selected home run is caught by a fan? (Type an integer or a decimal. Do not round.) Part 2 (b) Of the 1000 home runs, it was found that 263 were dropped when a fan made a legitimate attempt to catch the ball. What is the probability that a randomly selected home run is dropped? (Type an integer or a decimal. Do not round.) Part 3 (c) Of the 75 caught balls, it was determined that 31 were barehanded catches, 42 were caught with a glove, and 2 were caught in a hat. What is the probability a randomly selected caught ball was caught in a hat? Interpret this probability. Select the correct choice below
Let's go through each part step by step.
(a) To find the probability that a randomly selected home run is caught by a fan, we use the formula for probability:
[ P(\text{caught by fan}) = \frac{\text{Number of home runs caught by fans}}{\text{Total number of home runs}} ]
Given that 75 out of 1000 home runs were caught by fans:
[ P(\text{caught by fan}) = \frac{75}{1000} = 0.075 ]
(b) To find the probability that a randomly selected home run is dropped, we again use the probability formula:
[ P(\text{dropped}) = \frac{\text{Number of home runs dropped}}{\text{Total number of home runs}} ]
Given that 263 out of 1000 home runs were dropped:
[ P(\text{dropped}) = \frac{263}{1000} = 0.263 ]
(c) To find the probability that a randomly selected caught ball was caught in a hat, we use the formula:
[ P(\text{caught in hat}) = \frac{\text{Number of home runs caught in a hat}}{\text{Total number of home runs caught}} ]
Given that 2 out of 75 caught balls were caught in a hat:
[ P(\text{caught in hat}) = \frac{2}{75} \approx 0.02667 ]
Interpretation: This probability means that if you randomly select one of the home runs that were caught by fans, there is approximately a 2.67% chance that it was caught in a hat. This indicates that catching a home run in a hat is a relatively rare occurrence compared to other methods of catching, such as using bare hands or gloves.