Expectanion value probabilities

[ParisSpart]

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?

 

[mfb]

The probability of getting k heads in 10 flips is not 0.57^k.

 

[ParisSpart]

0.43?

 

[mfb]

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.

 

[ParisSpart]

we don't have learned distrinutions in school yet...

 

[haruspex]

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?

 

[HallsofIvy]

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"?

 

[ParisSpart]

how i can solve it with distributions way?