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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?

Respuesta :

Answer:

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)

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