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28 January, 09:28

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?

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  1. 28 January, 10:18
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    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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