20% of customers at a restaurant order takeout meals. 77% of customers at the same restaurant pay with a credit card. Assume whether a customer orders a takeout meal is independent of whether the customer pays with a credit card. Answer the following for a randomly selected customer: What is the probability the customer ordered a takeout meal if the customer paid with a credit card?

the probability that the customer ordered a takeout meal if the customer paid with a credit card = 20% ( = % of customers at a restaurant order takeout meals)

Step-by-step explanation:

for events A and B, if both are independent, then one the probability that A happens is not affected by B and viceversa.

In probability terms

P (A|B) = P (A)

where P (A|B) = probability that event A happen knowing that B happened

In our case

event A = customer ordered a takeout meal

event B = customer paid with a credit card

therefore

P (A|B) = P (A) = 20%

strictly speaking, from Bayes's theorem:

P (A|B) = P (A∩B) / P (B)

P (A∩B) = probability that A and B happen

since both are independent P (A∩B) = P (A) * P (B), then

P (A|B) = P (A∩B) / P (B) = P (A) * P (B) / P (B) = P (A)

P (A|B) = P (A)