Historically, 5 percent of a mail-order firm's repeat charge-account customers have an incorrect current address in the firm's computer database. a)what is the probability that none of the next 12 repeat customers who call will have an incorrect address? b) One custome...
Tuesday, October 20, 2009 at 7:17pm by
probability of an incorrect address = 5/100
to have atleast 1 incorrect address out of the 12 customers (choice of 1 out of 12 customers)
12C1 x (5/100) =
(12!/ 1! 11!) (5/100)
= 12 x (5/100) = 60/100
So for none to be incorrect it will be (1 - Prob of atleast one to be incorrect)
1- (60/100) = 40/100 = 2/5
I beg to differ from Visper.
Probability of having a correct address is (95/100). So, probability of correct 12 in a row (or none incorrect) is (95/100)^12 = .54
So, probability of having AT LEAST one incorrect = 1-.54 = .44
Probability of having exactly one incorrect is 12C1 * (5/100) * (95/100)^11
= 12 * .05 * .5688 = .3413
I hope this helps.
To solve this problem, we need to use the concept of probability and apply it to the given situation.
a) To find the probability that none of the next 12 repeat customers will have an incorrect address, we need to calculate the probability of each customer having the correct address and then multiply them together.
Given that historically, 5 percent of the customers have an incorrect address, it means that 95 percent have the correct address. So the probability of a customer having the correct address is 0.95.
Since we want to find the probability for all 12 customers having the correct address, we can multiply the probabilities together:
Probability = (0.95) * (0.95) * (0.95) * ... * (0.95) (12 times)
Using exponential notation, we can write this as:
Probability = (0.95)^12
Calculating this, we get:
Probability = 0.5488
So the probability that none of the next 12 repeat customers will have an incorrect address is approximately 0.5488 or 54.88%.
b) To find the probability that exactly one customer out of the next 10 calls will have an incorrect address, we need to consider two cases: one customer has the incorrect address and the rest have the correct address.
The probability that one customer has the incorrect address is given by:
Probability = (0.05) * (0.95)^9
We multiply 0.05 (the probability of one customer having an incorrect address) with (0.95)^9 (the probability of the remaining 9 customers having the correct address).
Calculating this, we get:
Probability = 0.03038
So the probability that exactly one customer out of the next 10 calls will have an incorrect address is approximately 0.03038 or 3.038%.
This calculation assumes that the events (each customer's address being correct or incorrect) are independent, meaning that the probability of one customer having an incorrect address does not affect the probability of another customer having an incorrect address.