A restaurant in a fast food franchise has determined that the chance a customer will order a soft drink is 0.88. The probability that a customer will order a hamburger is 0.53.
The probability that a customer will order french fries is 0.49.
Complete parts a and b below.
a. If a customer places an order, what is the probability that the order will include a soft drink and no fries, if these two events are independent? (Round to four decimal places as needed.)
The probability is____________.
b. The restaurant has also determined that, if a customer orders a hamburger, the probability the customer will order fries is 0.71.
Determine the probability that the order will include a hamburger and fries. (Round to four decimal places as needed.)
The probability is________

Answer:

A) P(soft drink, hamburger, no fries) = 0.1912

B) P(fries and hamburger) = 0.3763

Step-by-step explanation:

A) Probability that the order will include a soft drink, a hamburger and no fries is;

P(soft drink, hamburger, no fries) = P(soft drink) x P(hamburger) x P(no French fries)

P(soft drink, hamburger, no fries) = 0.88 x 0.53 x (1 - 0.49) = 0.88 × 0.53 × 0.41 ≈ 0.1912

B) we are told that;

P(fries|hamburger)=0.71

Since P(fries|hamburger) = P(fries and hamburger)/P(hamburger)

Thus;

0.71 = P(fries and hamburger)/0.53

P(fries and hamburger)= 0.71 *0.53

P(fries and hamburger) = 0.3763

Final answer:

Question a's answer is 0.4488 meaning there's a 44.88% chance a customer will order a soft drink and no fries. For question b, the answer is 0.3763 meaning there's a 37.63% chance that an order will include a hamburger and fries.

Explanation:

To calculate probabilities of independent events, you simply multiply the probability of each event happening.

For question a. the probability of ordering a soft drink is given as 0.88, and the probability of ordering fries is given as 0.49. However, we want the probability of ordering a soft drink and not ordering fries, which means we need to take the complement of the fries event (1-0.49) which is 0.51. Multiply the probability of ordering a soft drink (0.88) with the probability of not ordering fries (0.51):

0.88 x 0.51 = 0.4488

Therefore the probability of a customer ordering a soft drink and no fries is 0.4488.

For question b. we are given the conditional probability that a customer will order fries given they have already ordered a hamburger, which is 0.71. To calculate the joint probability of both events (hamburger and fries), we must multiply the conditional probability by the probability of the hamburger event:

0.71 x 0.53 = 0.3763

Therefore the probability of an order including a hamburger and fries is 0.3763.

Learn more about Probability here:

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