Expectanion value probabilities

In summary, the problem involves flipping a coin 10 times with a probability of 0.57 for getting a crown. The result of the game is determined by the number of heads, with a payout of 2^k euros for k heads. To find the average profit, the expectation value needs to be calculated by summing up the probabilities of all possible outcomes. This can be done using distributions like binomial distribution, permutations and combinations, and binomial coefficients.
  • #1
ParisSpart
129
0
Flipping a coin 10 times. The currency brings crown with probability 0.57. If you bring a total of k heads they add 2 ^ k euros.

What is the average profit in this game?

i must find the expectanion value and i do this:

∑from k=1 to 10 --->((0.57)^k)*(2^k) =22.0445164

i think that my solve is not correct any ideas?
 
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  • #2
The probability of getting k heads in 10 flips is not 0.57^k.
 
  • #3
0.43?
 
  • #4
No, and guessing will not help.
This is a basic problem in statistics, you should know which distribution you have to use.

As a general remark: you should always check if your values, results, ... are plausible. Please do this before you ask questions.
As an example, the probability to get k times heads in 10 flips is certainly different than the probability to get k times heads in 1 flip. Therefore, the value has to depend on the number of flips in some way, otherwise it cannot be right.
 
  • #5
we don't have learned distrinutions in school yet...
 
  • #6
in your sum, you need the probability of exactly k heads. So you have to take into account that 10-k are not heads. Also, you don't care which of the 10 are heads. how many different possibilities are there for which are?
 
  • #7
ParisSpart said:
we don't have learned distrinutions in school yet...
That makes this problem very difficult! I imagine you have learned enough to know that the probability of all 10 being crowns will be (.57)10 and the probability that all ten are not crowns will be (1- .57)10= (.43)10. But the probability that the first flip is a crown and the rest are not is (.57)(.43)(.43)(.43)(.43)(.43)(.43)(.43)(.43)(.43)= (.57)(.43)9 while the probability of "first not a crown, second a crown, then the rest not crowns" is (.43)(.57)(.43)(.43)(.43)(.43)(.43)(.43)(.43)(.43)= (.57)(.43)9 so that the probability of "one crown, nine non-crowns" is 10(.57)(.43)9.

And things like "four crowns, 6 non-crowns" get much more complicated as the possiblities increase. Are you sure you have not learned things like "permutations and combinations", "binomial coefficents", and "binomial distributions"?
 
  • #8
how i can solve it with distributions way?
 

FAQ: Expectanion value probabilities

1. What is the concept of expectation value probabilities?

Expectation value probabilities, also known as expected values, are a way to quantitatively describe the likelihood of a specific outcome in a probabilistic system. It is the average value of a random variable over multiple trials or experiments.

2. How is expectation value calculated?

Expectation value is calculated by multiplying each possible outcome by its respective probability and summing all the products together. This can be represented mathematically as E(X) = ∑xP(x), where E(X) is the expectation value, x is the possible outcomes, and P(x) is the probability of each outcome.

3. What is the significance of expectation value probabilities in scientific research?

Expectation value probabilities are important in scientific research as they allow for a more accurate and objective understanding of the outcomes of experiments or observations. They provide a way to predict the most likely outcome and can be used to make informed decisions and draw conclusions from data.

4. Can expectation value probabilities be applied to any type of data?

Yes, expectation value probabilities can be applied to any type of data that follows a probabilistic distribution, such as binomial, normal, or Poisson distributions. It can also be applied to continuous data by using probability density functions.

5. How can expectation value probabilities be used in decision-making processes?

Expectation value probabilities can be used to calculate the expected return or outcome of a decision by considering the potential outcomes and their respective probabilities. This can help in making data-driven and rational decisions, especially in situations where there is uncertainty or risk involved.

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