Respuesta :
The expected value is $0.11.
The probability that the player will make the next free throw is 233/402. The probability that the next 3 are made will be (233/402)^3. To find the expected value of this, we multiply by the winnings we would have in this case, 166. So far we have:
((233/402)^3)(166)
The probability that the next 3 are not made is 1-((233/402)^3). Multiply this by the loss, -40, to get its expected value. This gets us to:
((233/402)^3)(166)-(1-((233/402)^3)).
This comes out to $0.11.
The probability that the player will make the next free throw is 233/402. The probability that the next 3 are made will be (233/402)^3. To find the expected value of this, we multiply by the winnings we would have in this case, 166. So far we have:
((233/402)^3)(166)
The probability that the next 3 are not made is 1-((233/402)^3). Multiply this by the loss, -40, to get its expected value. This gets us to:
((233/402)^3)(166)-(1-((233/402)^3)).
This comes out to $0.11.
Answer:
There expected value of the proposition for you is -11 cents, that is, you are expected to lose $0.11.
Step-by-step explanation:
The first step to solve this problem is finding the probability that he makes 3 of his next 3 free throws.
The problem states that he makes 233 out of 402 free throws. This means that the probability that he makes a free throw is [tex]p = \frac{233}{402} = 0.5796[/tex].
The probability that he makes his next 3 free throws is [tex]P = 0.5796^{3} = 0.1947[/tex]
if the player makes the next 3 free throws, i will pay you $166. otherwise you pay me $40.
There is a 19.47% probability of him making the next three free throws. This means that there is a 19.47% probbability of you losing $166.
There is a 100-19.47 = 80.53% probability of him not making the next three free throws. This means that there is an 80.53% probability of you winning $40.
So, for you, the expected value of the proposition is:
[tex]E = 0.8053*(40) -166*(0.1947) = -0.11[/tex]
There expected value of the proposition for you is -11 cents.
