Question

Among all the car accidents last year, 492 deaths were reported in
the road of which 240 wore belts and 252 wore no belts. Of the 2334
people involved in serious accidents 1945 wore seat belts and the rest
no
to. Calculate the probability of dying by not wearing a belt

b. Calculate the probability of dying if you wear the belt

c. If a person dies in a car accident; What is the probability of
who will wear a seat belt?

Answer 1

Given the total number of deaths in car accidents = 492. Now, number of people died due to car accidents wearing belt = 240. Number of people died due to car accidents not wearing belt = 252.

As all our three questions are regarding death thus, we are not considering the case of serious accident.

We know, Probability of any event = (Number of favorable outcomes)/(Total number of possible outcomes). ---------(1)

From conditional probability we have, P(A|B) = P(A B)/P(B), where, event B is given and we have to find the probability of event A. --------(2)

a) We have to calculate the probability of dying by not wearing a belt.

Number of people died = 492. Thus, total number of possible outcomes = 492.

Now, number of people who died by not wearing a belt = 252. Thus, number of favorable outcomes = 252.

Thus, from (1), the required probability = 252/492 = 0.5122(rounded up to four decimal places).

Thus, the probability of dying by not wearing a belt = 0.5122 .

b) Here, we have to find the probability of dying if we wear the belt.

Total number of people died = 492. Thus, total number of possible outcomes = 492.

Now, number of people who died by wearing a belt = 240. Thus, number of favorable outcomes = 240.

Thus, from (1), the required probability = 240/492 = 0.4878(rounded up to four decimal places).

Thus, the probability of dying if we wear the belt = 0.4878 .

c) Here, it is given that if a person dies in a car accident, we have to find the probability of wearing a seat belt. Here, we will use conditional probability. Thus, from (2), here, the given event B is the event that a person dies in a car accident and the event A is the event of wearing a seat belt.

Thus, P(A B) = Number of people who died in the car accident wearing seat belt = 240

P(B) = Number of people died in car accident = 492.

Thus, from (2), the required probability, P(A|B) = 240/492 = 0.4878(rounded up to four decimal places).

​​​​​​​Thus, if a person dies in a car accident, the probability of wearing a seat belt = 0.4878 .