Be sure to show work and circle answer(s). At Pierre\'s Coffee Shop, 58% of cust

Question

Be sure to show work and circle answer(s). 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. a) What is the probability that a customer will order tea or orange juice? (4 pts) 1. b) What is the probability that five straight customers will rder 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

a) Probability that the customer will order tea is 25/100 = 0.25

Probability that the customer will order orange juice is 13/100 = 0.13

Since the individual customer do not order more than one drink

P ( customer will order tea and coffee)

= P (tea orange juice)

= 0

P( customer will order tea or orange juice )

= P (customer will order tea) + P (customer will order orange juice) – P ( customer will order tea and coffee)

=0.25 + 0.13 - 0

=0.38

b) P (five straight customers will order a muffin)

= P( first customer will order a muffin) x P( second customer will order a muffin) x ……………..x     P(fifth customer will order a muffin)

= ( 0.27 )5

               = 0.001435

c) P ( first customer will order Danish or bagel )

= P (first customer will order Danish ) + P (first customer will order bagel)

= 0.46 + 0.18

=0.64

P ( second customer will order a muffin or a bagel)

= P (second customer will order muffin ) + P (second customer will order bagel)

= 0.27+0.18

= 0.45

P(first customer will order Danish or bagel and second customer will order a muffin or a bagel)

= P ( first customer will order Danish or bagel ) x P ( second customer will order a muffin or a bagel)

=0.64 x 0.45

=0.288

d) P( customer do not order anything to eat )

= 9/100 = 0.09

Suppose, X is a random variable denoting number of customers do not order anything to eat.

Here, X follows binomial distribution.

n=number of customer entered = 4

P( X 1) = 1 - P (X <1) = 1 – P ( X=0) = 1 – 4C0 (0.09)0 ( 1-0.09)4-0

                                                                       = 0.31425039

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.