The data on the right represent the number of traffic fatalities by seat location and gender. Determine P(male) and P(male|passenger). Are the events "male" and "passenger" independent? Female Male Total Passenger 32,906 11,713 44,619 Driver 6,481 6,343 12,824 Total 39,387 18,056 57,443 Question content area bottom Part 1 Determine P(male). P(male)equals enter your response here (Round to three decimal places as needed.) Part 2 Determine P(male|passenger). P(male|passenger)equals enter your response here (Round to three decimal places as needed.) Part 3 Are the events "male" and "passenger" independent? A. Yes. The occurrence of the event "passenger" does not affect the probability of the event "male." B. Yes. The occurrence of the event "passenger" affects the probability of the event "passenger." C. No. The occurrence of the event "passenger" does not affect the probability of the event "male." D. No. The occurrence of the event "pass
To solve the problem, we will calculate the probabilities step by step.
To find ( P(\text{male}) ), we use the formula:
[ P(\text{male}) = \frac{\text{Number of males}}{\text{Total number of individuals}} ]
From the data provided:
Now we can calculate ( P(\text{male}) ):
[ P(\text{male}) = \frac{18,056}{57,443} \approx 0.314 ]
To find ( P(\text{male} | \text{passenger}) ), we use the formula:
[ P(\text{male} | \text{passenger}) = \frac{\text{Number of male passengers}}{\text{Total number of passengers}} ]
From the data provided:
Now we can calculate ( P(\text{male} | \text{passenger}) ):
[ P(\text{male} | \text{passenger}) = \frac{11,713}{44,619} \approx 0.262 ]
To determine if the events "male" and "passenger" are independent, we check if:
[ P(\text{male} | \text{passenger}) = P(\text{male}) ]
From our calculations:
Since ( P(\text{male} | \text{passenger}) \neq P(\text{male}) ), the events are not independent.