There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the probability that the first such rejection occurs within the first 20 Visa transactions?
A).1362
B).4000
C).3324
D).4538

Question

Quizplus · Accepted Answer

The number of trials, n = 20 
Probability of rejection, p = 0.02 
Let X be the number of trials until the first rejection occurs. X follows a geometric distribution, with the probability mass function: 
P(X=k) = (1-p)^(k-1)*p

The probability that the first rejection occurs within the first 20 Visa transactions is: 
P(X <= 20) 
= P(X=1) + P(X=2) + ... + P(X=20) 
= Σ(1-p)^(k-1)*p, k=1 to 20

Using the formula for the sum of a geometric series, we get: 
P(X <= 20) = 1 - (1-p)^20 
= 1 - 0.98^20 
= 0.332438

Therefore, the answer is choice C: 0.3324.

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