Answer to Question #149529 in Statistics and Probability for Richa Patel

Question

Q.8 In a staff meeting called to address the problem of returned cheques at the supermarkets where you are interning as a financial analyst, the bank reports that 12 percent of all cheques are returned for insufficient funds, and of those, in those 50 percent of cases, there was cash given back to the customer. overall ,10 percent of customers ask for cash back at the end of their transaction with the store. For 1,000 customer visits, how many transactions will involve:
(f) insufficient funds? (g) Cash back to the customer? (h) Both insufficient funds and cashback? (i) Either insufficient funds or cash back?

Answer 1

We have that

P(insufficient funds) = 12% = 0.12

P(cashback | insufficient) = 50% = 0.5

P(cashback) = 10% = 0.1

n = 1000

(f) insufficient funds:

1000 * 0.12 = 120

(g) cashback to the customer:

1000 * 0.1 = 100

(h) both insufficient funds and cashback:

P(insufficient and cashback) = P(cashback | insufficient) * P(insufficient)=0.5 * 0.12=0.06

1000 * 0.06 = 60

(i) either insufficient funds or cashback:

P(insufficient or cashback) = P(insufficient) + P(cashback) – P(insufficient and cashback) = 0.12 + 0.1 – 0.06 = 0.16

1000 * 0.16 = 160

Answer:

f) 120

g) 100

h) 60

i) 160