Question

The data on the right represent the number of traffic fatalities by seat location and gender. Determine ​P(​) and ​P(​|​). Are the events ​"​" and ​"​" ​independent? Total Total Determine ​P(​). ​P(​) . 318 ​(Round to three decimal places as​ needed.) Determine ​P(​|​). ​P(​|​) . 264 ​(Round to three decimal places as​ needed.) Are the events ​"​" and ​"​" ​independent? A. Yes. The occurrence of the event ​"​" affects the probability of the event ​"​." B. No. The occurrence of the event ​"​" affects the probability of the event ​"​." C. No. The occurrence of the event ​"​" does not affect the probability of the event ​"​." D. Yes. The occurrence of the event ​"​" does not affect the probability of the event ​"​."

Answer 1

Answer:

The probability of selecting a male is 0.3151.

The events "male" and "driver" are not independent.

The correct option is B.

Step-by-step explanation:

The missing data is as follows:

                    Female          Male          Total

Driver            32759          11715          44474

Passenger      6534           6361          12895

Total              39293         18076          57369

The complete question is:

Determine ​P(​male) and ​P(male​|driver​). Are the events ​"male​" and ​"​driver" ​independent?

Solution:

Compute the probability of selecting a male as follow:

$P(M)=\frac{n(M)}{N}=\frac{18076 }{57369}=0.3151$

Thus, the probability of selecting a male is 0.3151.

Compute the probability of selecting a male given that he is a driver as follows:

$P(M|D)=\frac{P(M\cap D)}{P(D)}=\frac{n(M\cap D)}{n(D)}=\frac{11715 }{44474}=0.2634$

Two events, say A and B, are independent if:

P (A|B) = P(A)

Here, P (M|D) ≠ P (M)

Thus, the events "male" and "driver" are not independent.