An insurance company classifies its customers into three groups,a,b and c. Groups a accounts for 20% of the total custermers, groupe b accounts 40%, and accounts for 40%. For people in groupe a,b and c, the probabilities of having an accident in one year are 0,0.1,and 0.2 respectively . For any customer, the probability of having more than one accident in one year is zero. (a) a customer is chosen at tandem. Given this customer is from groupe c.
To answer this question, we need to calculate the probability that the chosen customer from group C had an accident in one year.
Given the information provided, we know that the probability of having an accident in one year for group C is 0.2.
To calculate the probability that a customer chosen at random is from group C, we can use the concept of conditional probability.
Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, we want to calculate the probability that the customer chosen is from group C, given that the customer had an accident in one year.
The formula for conditional probability is as follows:
P(A|B) = P(A and B) / P(B)
In this case, we want to calculate P(C|A), which represents the probability of being from group C, given that the customer had an accident in one year.
P(C|A) = P(C and A) / P(A)
We already know P(A) = 0.2, and P(A and C) = 0.2 (since the probability of having more than one accident is zero, the events "having an accident" and "being in group C" are the same).
Plugging these values into the formula, we get:
P(C|A) = 0.2 / 0.2 = 1
Therefore, the probability that a customer chosen at random is from group C, given that the customer had an accident in one year, is 1 or 100%.