A student of mine was asked this question in an interview Co

A student of mine was asked this question in an interview. \"Consider the following game: A cup is filled with 100 pennies. The cup is shaken, and the pennies are poured onto a table. If at least 60 of the pennies are Heads, you win $20. Otherwise, you lose $1. Is this a good game to play?\" (That is does it have a positive expected value?). Answer this using simulation in R. Determine how much you would win or lose. Does it appear to be a fair game?

Solution

calculating this many pennies with the binomial is a pain, which is why we\'d use a normal approximation. Here, we let mu=n*p = 100*.5 = 50 (the exected number of pennies to end up heads) and pi= sqt(n*p*q)=sqt(100*.5*.5)=5

then we can find a Z-score, nothing tht above 60 heads is what peaks our interest.

Z = (60-50)/5=2

Nothing on our Z-score hart that the area to the area to the right of Z = 2 is 0.0228, this means we have a probability of 2.28% to land 60 or more heads.

Thus, the expected earnings from the game is 0.0228*($20)-0.9772*($1) = -0.5212 . . which means this is a bad game to be playing, but a good to hustle your frinds out of $$$

Source(s):

m\'noggin