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 SX that would make this a profitable bet in the long run? b.

Explanation / Answer

a) here probbability to at least once dunk your professor =1-P(not able to dunk in all 3 attempts) =1-(0.75)3

=0.5781

as probability of that is higher than 0.5 hence this is a profitable bet

b)

for profitable bet : expected win >expeced loss

x*0.5781 >5*(1-0.5781)

X>$3.65

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.