Question

A store specializing in mountain bikes is to open in one of two malls. If the first mall is​ selected, the store anticipates a yearly profit of $900,000 if successful and a yearly loss of $300,000 otherwise. The probability of success is one half. If the second mall is​ selected, it is estimated that the yearly profit will be $600,000 if​ successful; otherwise, the annual loss will be $180,000. The probability of success at the second mall is three fourths.

Complete parts​ (a) through​ (c) below:
(a) what is the expected profit for the first mall?
(b) What is the expected profit for the second mall?
(c) Which mall should be chosen in order to maximize the expected profit?

A. the first mall should be chosen in order to maximize profit.
B. the second mall should be chosen in order to maximize profit.
C. either of the two malls may be chosen; the profit will be the same.

Answer 1

(a)Expected Profit of the first mall=$300,000

(b)Expected Profit of the second mall=$405,000

(c)(B)The second mall should be chosen in order to maximize profit.

Explanation:

(a)First Mall

Yearly profit = $900,000

P(Success)=0.5

Yearly loss = $300,000

P(Failure)=0.5

Expected Profit = (900000*0.5)+(-300000*0.5)=$300,000

(b)Second Mall

Yearly profit = $600,000

P(Success)=0.75

Yearly loss = $180,000.

P(Failure)=0.25

Expected Profit=(600000*0.75)+(-180000*0.25)=$405,000

(c)The second mall should be chosen in order to maximize profit.

Answer 2

a) Expected profit = $300,000

b) Expected profit = $405,000

c) The second mall should be chosen in order to maximize the expected profit

Explanation:

If the first mall is selected:

Anticipated profit on success = $900,000

Anticipated loss on failure = $300,000

Probability of success, p = 1/2

Probability of failure, q = 1-p = 1-1/2

q = 1/2

If the second mall is selected:

Anticipated profit on success = $600,000

Anticipated loss on failure = $180,000

Probability of success, p = 3/4

Probability of failure, q = 1-p = 1-3/4

q = 1/4

a) Expected profit for the first mall:

Expected profit = (p*profit) - (q*loss)

Expected profit =(1/2 * 900000) - (1/2 * 300000)

Expected profit = $300,000

b) Expected profit for the second mall:

Expected profit = (p*profit) - (q*loss)

Expected profit =(3/4 * 600000) - (1/4 * 180000)

Expected profit = $405,000

c) The second mall should be chosen in order to maximize the expected profit