Question

Q3. A simple restaurant tracked the sales of burger (population A) and/or fries (population B) as shown in the diagram. 10% A B (55%) (20%) In this sample, are the events "burgers" and "fries" mutually exclusive? (Explain your answer) 15% Find the probability that a randomly selected customer from this sample bought a burger OR bought fries (Please show formulas and calculations) .

Answer 1

3)

A : sale of burger

B : sale of fries

P(A) = 0.55

P(B) = 0.20

For the events A and B to be mutually exclusive

P(A ∩ B) = 0               that is events A and B cannot occur together

But, from the Venn diagram,

P(A ∩ B) = 10% = 0.10 ≠ 0

P(A ∩ B) ≠ 0

Hence, the events burgers and fries are not mutually exclusive

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To find P(randomly selected person bought a burger or bought fries)

that is to find P(A U B)

By inclusion exclusion rule

P(A U B) = P(A) + P(B) - P(A ∩ B)

               = 0.55 + 0.20 - 0.10                     (... From the Venn diagram)

               = 0.65

P(randomly selected person bought a burger or bought fries) = $\mathbf{0.65}$

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