4. Binomial Random Variable: Suppose that at FIU Homecoming this year, there is

Question

4. Binomial Random Variable: 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! Suppose that your probability of hitting the lever each time is 0.25. Your friend offers you a bet of $5 that you cannot dunk your professor at all. 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? a. 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 $X 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

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