Question

Calculate the expected value with the information given.

1) You are considering making an investment in Boeing stock. You

figure that there is a 45% chance the stock will increase in price by

$5 in a year, that there is a 20% chance that it will stay the same

price in a year, and that if the stock decreases in value it will

only decrease by $3 in a year. What is the expected profit per stock

invested?

2) You are, again, playing a Role Playing Game with friends. You just

learned a new ability and want to figure out how much damage on

average that it will do. If you roll a 1-12 on a twenty sided die you

will do 6 damage, and if you roll a 13 or higher on a twenty sided

die you will do 10 damage. How much damage will you expect to do each

attack?

Answer 1

1)

X : Profit per stock invested.

45% chance the stock will increase in price by $5 in a year ; X = 5 ; P(X=5) = 45/100=0.45

20% chance that it will stay the same price in a year ; X=0 ; P(X=0) =20/100 = 0.20

Chance that the stock decreases in value

= 100 - [chance the stock will increase in price+chance that it will stay the same price]

= 100 -[45+20]=35%

and that if the stock decreases in value it will only decrease by $3 in a year ; X=-3 ; P(X=-3) = 35/100 =0.35

The expected profit per stock invested = E(X)

Expected profit per stock invested = $1.20

2)

X: Damage you will do

Total Number of sides on 20 sided die = 20

Number sides with 1-12 =12

Number sides with 13 or higher(13-20) = 8

Probability of rolling a 1-12 on a twenty sided die

= Number sides with 1-12 / Total Number of sides on 20 sided die = 12/20=3/5

Probability of rolling a 13 or higher on a twenty sided die

= Number sides with 13 or higher(13-20) / Total Number of sides on 20 sided die = 8/20=2/5

If you roll a 1-12 on a twenty sided die you will do 6 damage : X=6 ; P(X=6) = 3/5

If you roll a 13 or higher on a twenty sided die you will do 10 damage: X=10 ; P(X=10) =2/5

damage will you expect to do each attack = E(X)

damage will you expect to do each attack = 38/5 = 7.6