At Pierre\'s Coffee Shop, 58% of customers order coffee, 25% order tea, and 13%

Question

At Pierre's Coffee Shop, 58% of customers order coffee, 25% order tea, and 13% order orange juice, while 4% do not order anything to drink. In addition, 27% order a muffin, 46% order a danish, and 18% order a bagel, while 9% do not order anything to eat. Finally, 21% of customers order both coffee and a danish, and 54% of people order a bagel given that they have ordered tea. Assume that an individual customer will not order more than one drink or more than one breakfast roll. Also assume that the customers are independent of each other.

Explanation / Answer

D) P(at least one of them will not order anything) = 0.09 * 0.91 * 0.91 * 0.91 + 0.09 * 0.09 * 0.91 * 0.91 + 0.09 * 0.09 * 0.09 * 0.91 + 0.09 * 0.09 * 0.09 * 0.09 = 0.075

E) P(Danish|coffee) = P(Danish and coffee)/P(coffee)

= 0.21/0.58 = 0.362

F) P(coffee or Danish) = P(coffee) + P(Danish) - P(coffee and Danish) = 0.58 + 0.46 - 0.21 = 0.83

G) P(bagel | tea) = P(bagel and tea)/P(tea)

Or, 0.54 = P(bagel and tea)/0.25

Or, P(bagel and tea) = 0.54 * 0.25 = 0.135

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