A fast-food restaurant has determined that the chance a customer will order a soft drink is 0.90. The proba- bility that a customer will order a hamburger is 0.60. The probability that a customer will order french fries is 0.50. a) If a customer places an order, what is the probability that the order will include a soft drink and no fries if those two events are independent? b) The restaurant has also determined that if a customer orders a hamburger, the probability the customer will order fries is 0.80. Determine the probability that the order will include a hamburger and fries.

(a) The probability that the order will include a soft drink and no fries is 0.45.

(b) The probability that the order will include a hamburger and fries is 0.48.

Explanation:

Let the events be denoted as follows:

S = an order of soft drink

H = an order of hamburger

F = an order of french fries.

Given:

P (S) = 0.90

P (H) = 0.60

P (F) = 0.50

(a)

It is provided that the event of ordering a soft drink and fries are independent.

If events A and B are independent then the probability of event (A ∩ B) is:

Compute the probability that the order will include a soft drink and no fries as follows:

Thus, the probability that the order will include a soft drink and no fries is 0.45.

(b)

It is provided that the conditional probability that a customer will order fries given that he/she has already ordered a hamburger as, P (F|H) = 0.80.

The conditional probability of an event B given another event A has already occurred is:

Compute the probability that the order will include a hamburger and fries as follows:

Thus, the probability that the order will include a hamburger and fries is 0.48.