Question

1. An investment will produce a profit of $1220 with probability 0.2, $980 with probability 0.6, and $320, with probability 0.2. What is the expected profit?

(a.)$896

(b.)$1003

(c.)$974

(d.)$924

2. Project 1 generates revenue of $500 with probability 0.72 and $345 with probability 0.28. Project 2generates revenue $990 with probability 0.5 and revenue $155 with probability 0.5. If Mr. W wants to maximize his expected revenue, he should

(a.)choose Project 1

(b.)choose Project 2

(c.)choose either project because of they have the same exp. revenue

(d.)none of the above

3. The expected value of lottery A and B are the same. A pays $300 with probability 0.75 and $700 with probability 0.25. B pays $250 with probability p, and $550 with probability 1‐p. What is p?

(a.)0.25

(b.)).35

(c.)0.45

(d.)0.55

(e.)None of the above

4. George faces a gamble where he will win $200 with probability 0.4 and $X with probability 0.6. The expected value of the gamble is $140. Then $X is

(a.)$90

(b.)$100

(c.)$190

(d.)$290

Answer 1

1. Option A. $896.

Explanation: Expected profit = $1220 * 0.2 + $980 * 0.6 + $320 * 0.2 = $244 + $588 + $64 = $896.

2. (b.)choose Project 2

Explanation: Expected profit from project 1 = $500 * 0.72 + $345 * 0.28 = $360 + $96.6 = $456.6

Expected profit from project 2 = $990 * 0.50 + $155 * 0.5 = $495 + $77.5 = $572.5

Project B should be chosen as its expected value is greater.