Chapter 13.5, Problem 3CFU

To determine

To explain: The real life examples of conditional probability.

Answer to Problem 3CFU

Sales of car on a normal day and during Diwali. The loan given to a middle aged man, a young and senior citizen.

Explanation of Solution

Given information:

The term conditional probability.

Calculation:

Consider the term conditional probability.

Recall that probability of an event E is $P\left(\text{E}\right)=\frac{\text{number of outcome}}{\text{total number of outcome}}$ .

Recall that given an event Q, the conditional probability of event A is $P\left(A|Q\right)=\frac{P\left(A\text{ and Q}\right)}{P\left(Q\right)}$ where $P\left(Q\right)\ne 0$ .

Think of a company that sells car. The number of cars sold by company on a regular day is less than when sold during Diwali. This is a festival time so people buy new gifts for themselves and for their friends.

The probability of selling a car on day given that the day is Diwali.

Here we are given an event which is already happened that is occasion is Diwali.

If probability of selling a car is $32\%$ on a day and on Diwali the probability of selling a car is $68\%$ .

Similarly think of a bank that provided loan to people. Suppose there are three categories young, middle aged and old age. So there is a risk of providing loan to young as they are not much mature and also don’t have much assets to pay back loan. Also for old age, the certain demise of the person could be a problem. So, there is still a profit in providing loan to middle aged person. They have both assets and good time to pay back the loan.

The probability that there is no risk in providing the loan to the person given that the person is a middle aged person.

Thus, two real life situations are sales of car on a normal day and during Diwali. The loan given to a middle aged man, a young and senior citizen.