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

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

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is