A bank has studied its chequing accounts and found that 96% of all chequing acco

Question

A bank has studied its chequing accounts and found that 96% of all chequing accounts have been open for at least one year, the remaining percentage of chequing accounts have been open for less than a year. The bank also determined that for all chequing accounts that have been open for less than one year, the percentage of cheques returned due to insufficient funds is 5%. For chequing accounts that have been open for at least one year, only 1% of cheques were returned due to insufficient funds.

(a) What is the probability that a cheque processed by this bank will be returned due to insufficient funds? I got the answer to be 0.0116 but I don't understand how to do part b

(b) If a cheque is returned due to insufficient funds, what is the probability that it came from a bank account that has been open for less than one year?

Explanation / Answer

Let

L = less than 1 year
M = more than 1 year
I = insufficient funds

a)

P(I) = P(L) P(I|L) + P(M) P(I|M)

= (1-0.96)*(0.05) + (0.96)*(0.01)

= 0.0116 [ANSWER]

**********

b)

P(L|I) = P(L) P(I|L) / P(I) = (1-0.96)*(0.05)/0.0116 = 0.172413793 [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.