At a restaurant, 80 percent of the diners are new customers p(n)=0.8, while 20 percent are regular customers p(n’)=0.2. and, 50 percent of the new customers pay by credit card p(c|n)=0.5, in contrast, 70 percent of the regular customers make payments by credit card p(c|n’)=0.7. what is the probability that a customer is new if he/she pays by credit card, p(n|c)? select one:
a. 0.5400
b. 0.5000
c. 0.7407
d. 0.8000

c. 0.7404

Step-by-step explanation:

We can use Bayes Formula,

We know every single value of that expression except P(C). We can calculate C by dividing into 2 cases: if the customer is new or not.

By the total probability theorem, we  know that P(C) = P(C|N)*P(N) + P(C|N')*P(N') = 0.5*0.8 + 0.7*0.2 = 0.4+0.14 = 0.54

We replace P(C) on the equation above and we obtain

Thus, P(N|C) = 0.7407. Answer c is correct

I hope this helped you!

step-by-step explanation:

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