Question

1) A Texas oil drilling company has determined that it costs $25,000 to sink a test well. If oil is hit, the revenue for the company will be $500,000. If natural gas is found, the revenue will be $150,000. If the probability of hitting oil is 3% and of hitting gas is 6%, find the expected value of sinking a test well.

2) Assume that for the next heavyweight fight the odds of Mike Tyson winning are 15 to 2. A gambler bets $10 that Mike Tyson will lose. If Mike Tyson loses, how much can the gambler hope to receive?

Answer 1

Question (1)

There are three outcomes on sinking a well,

1. Oil is Hit

2. Natural Gas is found

3 If nothing is hit

The table below gives us the expected value

Scenario	Revenue	Revenue - Cost	Probability	Probability * (Revenue - Cost)
Oil is Hit	500000	475000	0.03	14250
Natural gas is found	150000	125000	0.06	7500
If nothing is hit	0	-25000	0.91	-22750
				Probability * (Revenue - Cost) = -1000

Here the Expected value of sinking a test well = Probability * (Revenue - Cost) = -1000

Question (2)

For the next heavyweight fight the odds of Mike Tyson winning are 15 to 2

The formoa for convering odds ratio to probability is as below

Probability p = (Odds ratio) / (1 + odds ratio)

Here odds ration for Mike Tyson winning = 15/2

So Probability of Mike Tyson winning = (15/2) / (1+15/2)

= (15/2) / (17/2)

= 15/17

   Probability of Mike Tyson losing = 1 - (15/17)

= 2/17

So odds of Mike losing tge fight is 2 to 15

Total return based on the number of odds = Stake * odds + Stake

Here he bets $10 that Mike tyson loses

So His total treturn will be = 10*(2/15) + 10

= (20/15) + 10

= 1.3333 + 10

= $11.3333

So The gambler hopes to receive $11.333