B3. (a) A coffee shop believes that 60% of its coffee orders are takeaway. i) If

Question

B3. (a) A coffee shop believes that 60% of its coffee orders are takeaway. i) If 10 customers enter the store. What is the probability exactly four customers order their coffee for takeaway? - exactly six customers order their coffee for takeaway? - no more than eight customers order their coffee for takeaway? i) What is the probability that exactly 7 customers have their coffee in the shop? ) What is the probability that you have to wait until the 4th customer before a customer orders their coffee takeaway?

Explanation / Answer

B3 (a) Pr(Coffee orders are takeaay) = 0.60

(i) Number of customers = 10

Let say X are number of customers out of 10 order their coffeee for takeaway.

(a) Pr(X = 4) = BIN(X = 4; 10 ; 0.60) = 10C4 (0.60)4 (0.40)6 = 0.1115

(b) Pr(X = 6) =  BIN(X = 6; 10 ; 0.60) = 10C6 (0.60)6 (0.40)4 = 0.2508

(c) Pr(X<=8) = BIN(X <=8; 10; 0.60)

from Binomial Table

BIN(X <=8; 10; 0.60) = 0.9536

(ii) If Pr(takeaway) = 0.60

then Pr(Coffee at the shop) = 1 - 0.60 = 0.40

so let say Y is the number of people who drink coffee at the shop

Pr(Y = 7) = BIN (Y = 7; 10; 0.4) = 10C7 (0.60)3 (0.40)7 = 0.0425

(iii) Here Pr(Takeaway) = 0.60

so Probability that we have to wait until the 4th customer before a customer orders their coffee takeaway will mean that starting three customers drank coffee in the shop and 4th one is a takeaway.

Pr(4th one is a takeaway) = Pr(all intial 3 customer drink coffee in shop) * Pr(4th one takeaway)

= (0.4)3 * 0.6

= 0.0384

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