Problem 2 (20 points). Suppose that at FIU Homecoming this year, there is an eve
ID: 3339181 • Letter: P
Question
Problem 2 (20 points). Suppose that at FIU Homecoming this year, there is an event called "Dunk your Professor" You have three chances to throw a ball and hit a lever so that your professor will fall into the pool and get wet. You can dunk your professor a maximum of three times. Fun! a) Suppose that your probability of hitting the lever is 0.3. Your friend offers you a bet of $5 that you cannot dunk your professor. You win $5 if you dunk your professor at least once and lose $5 if you do not dunk your professor at all. Is this a profitable bet? Suppose that you win $X if you dunk your professor at least once and lose $5 if you do not dunk your professor at all. What is the minimum SX that would make this a profitable bet in the long run? b)Explanation / Answer
A) P(not dunking professor) = 0.7x0.7x0.7 = 0.343
So, P(dunking professor) = 1 - 0.343 = 0.657
P(dunking) is higher. So, the bet is profitable
B) Let X be the minimum value of X
At the break even point, 0.343x5 = 0.657X
X = $2.61
The minimum value for which it is profitable = $2.62