Question

The city of haunted hills is having a ghosting tournament. this is pretty much exactly like a fishing tournament, except that you catch ghosts instead of fish. The scooby gang is thinking of entering. velma wants to make sure the contest is worth the $100.00 entry fee. If the team catches no ghosts, they lose the entire fee and the probability of this happening is about 1/3. if they catch just one ghost they win $50 which is actuallly a net loss of $50 because they don't get the entry fee back. and the probability is also 1/3. but if they catch two ghosts they win $200 with a probability of 1/6. and if they catch three ghosts they win $500 probability is 1/6. find the expected value of the entry fee for the ghosting contest and use this to explain why the scooby gang should not enter.

Answer 1

we can write the data in the following way

Winning amount($) x	Probability,P(x)
-100	1/3
-50	1/3
200	1/6
500	1/6

We know that the formula for the expected value is given as

where P(x) is the probability corresponding to each xi values.

setting the values, we get

this gives us

E[x]= -33.33 + -16.67 + 33.33 + 83.33

on adding, we get

E[x] = $66.67

Therefore, expected value is $66.67

So, it is not good for scooby gang to enter the tournament because the expected profit is less than the entry fee in the tournament, which means there is no good point in entering the tournament. This tournament can result in a net loss of $33.33 per match in a large sample size.