Answer to Question #127423 in Statistics and Probability for thiwan

Question

A fast-food restaurant has determined that the chance a customer will order a soft drink is 0.90. The probability 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 French fries if these two events are independent?

(b) The restaurant has also determined that if a customer orders a hamburger, the probability the customer will also order fries is 0.80. Determine the probability that the order will include a hamburger and fries.

Answer 1

Solutuon:

(a) Let A be the event that the order will include a soft drink.

Then P(A)=0.9.

Let B be the event that the order will include French fries.

Then P(B)=0.5.

Since these events are independent, then P(A$\overline{B}$ )=P(A)P($\overline{B}$ )

P($\overline{B}$)=1-P(B)=1-0.5=0.5

P(A$\overline{B}$ )=0.9$\cdot$0.5=0.45

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

(b) Let C be the event that the order will include hamburger.

Then P(C)=0.6.

"if a customer orders a hamburger, the probability the customer will also order fries is 0.80"

Then P(B|C)=0.8.

P(B$\bigcap$ C)=P(B|C)P(С).

P(B$\bigcap$C)=0.8$\cdot$0.6=0.48.

The probability that the order will include a hamburger and fries is equal 0.48.