A departmental store sends bills to charge its customers once a month. Past experience shows that 70% of its customers pay their first month bill in time. The store also found that the customer who pays the bill in time has the probability of 0.8 of paying in time next month and the customer who doesn't pay in time has the probability of 0.4 of paying in time the next month. Based on the above information, answer the following questions : (i) Let $E_1$ and $E_2$ respectively denote the event of customer paying or not paying the first month bill in time. Find $P(E_1)$, $P(E_2)$. (ii) Let A denotes the event of customer paying second month's bill in time, then find $P(A|E_1)$ and $P(A|E_2)$. (iii) Find the probability of customer paying second month's bill in time. OR (iii) Find the probability of customer paying first month's bill in time if it is found that customer has paid the second month's bill in time.

Year	Paper Code	Set	Position
CBSE 2024	Series Other	Set 1	Question 38
CBSE 2024	Series Other	Set 1	Question 36
CBSE 2024	Series Other	Set 1	Question 37

• Step 1: Stating the fundamental formula / law statement (+1 Mark)
• Step 2: Intermediate mathematical substitution or proof steps (+1 Mark)
• Step 3: Correct final value or conclusion with mandatory SI units (+1 Mark)