A survey involving 100 random Starbucks customers indicates that 70 customers or

Question

A survey involving 100 random Starbucks customers indicates that 70 customers order vanilla flavored drinks, 45 order extra hot drinks, and two third of the customers ordering extra hot drinks also order vanilla flavored drinks. Let event A be a customer ordering vanilla flavored drink and event B be a customer ordering extra hot drink. Construct the Venn Diagram and calculate the following: Find P(A) and P(B) Find P(AC) and 9(B degree) Find P(A B) and P(A B) Find P(A|B) and P(B|A) Are the events A and B mutually exclusive? Are the events A and B independent?

Explanation / Answer

n(A) = 70

n(B) = 45

n(A n B) = (2/3)45 = 30

a)P(A) = 70/100 = 0.7

P(B) = 45/100 = 0.45

b)

P(Ac) = 1- P(A) = 1-0.7 = 0.3

P(Bc) = 1-0.45 = 0.55

c)P(A n B) = n(A n B)/100 =0.30

n(A U B) = n(A) +n(B) -n(A n B) = 40+75-30 = 85

P(A U B) = 85/100 = 0.85

d)P(A/B) = P(A n B)/P(B) = 0.30/0.45 = 0.67

P(B/A) = P(A n B)/P(A) = 0.30/0.70 = 3/7 = 0.43

e)P(A n B) is not zero

so A and B are not mutulaly exclusive

f)P(A)*P(B) = 0.7*0.45 which is not equal to P(A n B) = 0.30

so A and B are not independent

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