Question

Consider the following game: A cup is filled with 100 pennies. The cup is shaken, and...

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. Use the normal approximation to the binomial, together with the expected value, to decide if this is a good game to play.

Math   Statistics-And-Probability   
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Answer #1

ANSWER::

mean number of heads =np=100*0.5 =50

std deviation =(np(1-p))1/2 = 5

hence probabilty of losing =P(X<=59)=P(Z<(59.5-50)/5)=P(Z<1.9)=0.9713

and probability of winning =1-0.9713 =0.0287

hence expected value =expected gain -expected lose =0.0287*20 -0.9713*1=-$30.970

as expected value is negative it is not a good game to play.

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