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. 1. a) What is the probability that a customer will order tea or orange juice? (4 pts) b) What is the probability that five straight customers will order a muffin? (4 pts) If two customers walk into the coffee shop, what is the probability that the first will order a danish or a bagel and the second will order a muffin or a bagel? (5 pts) c)

Explanation / Answer

Here, we are given that:

P( coffee) = 0.58
P( tea ) = 0.25
P( orange juice ) = 0.13
P( no drink ) = 0.04

Also, we are given that:

P( muffin ) = 0.27
P( danish ) = 0.46
P( bagel ) = 0.18
P( no eating ) = 0.09

P( coffee and danish ) = 0.21
P( bagel | tea ) = 0.54

a) Probability here is computed as:

P( tea ) + P( orange juice ) = 0.25 + 0.13 = 0.38

Therefore 0.38 is the required probability here.

b) Probability that five straight customers will order a muffin is computed as:

P( muffin ) * P( muffin ) * P( muffin ) * P( muffin ) * P( muffin )

= 0.275

= 0.0014

Therefore 0.0014 is the required probability here.

c) Probability that the first will order a danish or a bagel and second will order a miffin or a bagel is computed as:

= [ P( danish ) + P( bagel )] [ P( muffin ) + P( bagel ) ]

= ( 0.46 + 0.18 )*( 0.27 + 0.18 )

= 0.288

Therefore 0.288 is the required probability here.

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