The probability that a customer wants a replacement of a guaranteed pr

1.	The probability that a customer wants a replacement of a guaranteed product after 9 months is 0.2 . Then the probability that out of 10 customers at most 2 customers will desire for replacement after 9 months is (a) 4.04(0.8)8 (b) 8.08(0.8)8 (c) 2.36(0.8)8 (d) 3(0.8)8
Answer» Answer: (a) 4.04(0.8)⁸ Solution: Given that the probability that a customer wants a replacement of a guaranteed product after 9 months is 0.2 . Therefore, p = 0.2 and q = 1 − p = 1 − 0.2 = 0.8 . Let X denote the number of customers who wants replacement of their guaranteed product in out of those 10 customers. Since, each customer have independent opinion, therefore, the trials are Bernoulli trails. Clearly, X has a binomial distribution with n = 10 and p = 0.2 . Now, the probability that out of 10 customers at most 2 customers will desire for replacement after 9 months is P(X ≤ 2) = P(0) + P(1) + P(2) \(^{10}C_0p^0q^{10}\) + \(^{10}C_1pq^{9}\) + \(^{10}C_2p^2q^{8}\) = \((0.8)^{10}+10(0.2)(0.8)^9+45(0.2)^2(0.8)^8\) = \((0.8)^8(0.64+1.6+1.8)=4.04(0.8)^8\)

The probability that a customer wants a replacement of a guaranteed product after 9 months is 0.2 . Then the probability that out of 10 customers at most 2 customers will desire for replacement after 9 months is (a) 4.04(0.8)8 (b) 8.08(0.8)8 (c) 2.36(0.8)8 (d) 3(0.8)8

Answer»

Answer: (a) 4.04(0.8)⁸

Solution:

Given that the probability that a customer wants a replacement of a guaranteed product after 9 months is 0.2 .

Therefore, p = 0.2 and q = 1 − p = 1 − 0.2 = 0.8 .

Let X denote the number of customers who wants replacement of their guaranteed product in out of those 10 customers.

Since, each customer have independent opinion, therefore, the trials are Bernoulli trails.

Clearly, X has a binomial distribution with n = 10 and p = 0.2 .

Now, the probability that out of 10 customers at most 2 customers will desire for replacement after 9 months is P(X ≤ 2) = P(0) + P(1) + P(2)

\(^{10}C_0p^0q^{10}\) + \(^{10}C_1pq^{9}\) + \(^{10}C_2p^2q^{8}\)

= \((0.8)^{10}+10(0.2)(0.8)^9+45(0.2)^2(0.8)^8\)

= \((0.8)^8(0.64+1.6+1.8)=4.04(0.8)^8\)