math problem

Question

3. A game is played by selecting one bill at random from a bag that contains ten $1 bills, five $2 bills, three $5 bills, one $10 bill and one $100. The player gets to keep the selected bill. There is a $20 charge to play the game. What is the expected value?

b. Explain what the expected value calculated above (in Question 3) means?

 

c. An architect is considering bidding for the design of a new theatre. The cost of drawing plans and submitting a model is $15,000. The probability of being awarded the bid is 0.2 and anticipated profits are $80,000, resulting in a possible gain of this amount minus the $15,000 cost for the plans and models. What is the expected value if the architect decides to bid for the design?

Answer 1

Hi Tracey,

 

To calculate expected value (EV), there are only 3 steps

1) Calculate the profit from each event (in question 3a, it will be the bill you select minus the $20 cost of playing the game, so the profit from selecting a $1 bill is -$19, the profit from selecting a $2 bill is -$18, a $5 bill is -$15, a $10 bill is -$10, and a $100 bill is +$80)

2) Calculate the probability of each event happening (in question 3a, there are 20 bills in total, so the probability of choosing a $1 bill is 10/20, the probability of choosing a $2 bill is 5/20, a $5 bill is 3/20, $10 is 1/20, and $100 is 1/20)

3) Multiply each profit by it's probability (multiply what you got in step 1 by what you got in step 2), and add them all up

 

Answers to 3a and 3b

3a. (10/20 * -$19) + (5/20 * -$18) + (3/20 * $-15) + (1/20 * -$10) + (1/20 * $80) = -$12.75

3b. This means that you can expect to lose an average of $12.75 every time you play the game

 

 

Answer to 3c

3c. We perform the same calculations as we did for 3a by figuring out the profit from each event, the probability of each event occurring, multiplying them, and then adding up the results of the multiplications 

 

Expected value if the architect gets the bid: $80,000 - $15,000 = +$65,000

Probability of architect winning the bid: 0.2

 

Expected value if the architect loses the bid: - $15,000 
Probability of architect losing the bid: 0.8

 

Expected value for bidding = (0.2 * $65,000) + (0.8 * -15,000) = +$1,000