6. William works at West-Side Wanda\'s, a fast food franchise. He determines tha

Question

6. William works at West-Side Wanda's, a fast food franchise. He determines that the probability that customer orders French fries is .3, and the probability that a customer orders a soft drink is .55. The probability that they order a fries and a drink together is (.25).

a) Are they events "orders fries" and "orders soft drink" disjoint (mutually exclusive)?

b) Are they events "orders fries" and "orders soft drink" independent?

c) Assuming that customers order independently of one another, what is the probability that two customers don't order fries?

d) What is the conditional probability that a customer orders a drink, given that they have ordered fries?

e) What is the conditional probability that a customer orders fries, given that they have ordered a drink?

Explanation / Answer

b)No, the "orders fries" and "orders soft drink" is not independent, as P(F)*P(S)=0.3*0.55=0.165

But, P(F and S)=0.25 which is not equal to P(F)*P(S).

a)The two events "orders fries" and "orders soft drink" are not disjoint (mutually exclusive) as P(F and S) is not equal to zero.

d)The conditional probability that a customer orders a drink, given that they have ordered fries:

P(S given F)

=P(S and F)/P(F)

=0.25/0.3=0.83

e)The conditional probability that a customer orders fries, given that they have ordered a drink:

P(F given S)=P(F and S)/P(S)

=0.25/0.55

=0.45

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