Question 1044198: Lottery ticket claimed that one in nine ticket win a prize.
a)what is the probability that you win at least twice when you purchase ten tickets
b)what is the approximate probability that you win more than 120times if you purchase 900 tickets?
c)Of all awarded prizes,10% are worth $1000,20% are worth %100 and 70% are worth $10.Find the expected winning if you purchase a single ticket.
Answer by reviewermath(1029)   (Show Source):
You can put this solution on YOUR website! Q:Lottery ticket claimed that one in nine ticket win a prize.
a)what is the probability that you win at least twice when you purchase ten tickets
b)what is the approximate probability that you win more than 120times if you purchase 900 tickets?
c)Of all awarded prizes,10% are worth $1000,20% are worth %100 and 70% are worth $10.Find the expected winning if you purchase a single ticket.
Solution:
Let X = number of tickets that win a prize
a) X~Binomial(n = 10, p = 1/9)
The formula using a TI calculator is
1-binomcdf(10, 1/9, 1).
The formula using Excel is
=1-BINOMDIST(1,10,1/9,TRUE)
The result to 4 decimal places is 
b) X is approximately normal with mean 900(1/9) = 100 and variance
900(1/9)(8/9) = 800/9.
To correct for continuity, subtract 0.5 from X.
So the desired probability is P(X > 120.5).
Using a TI calculator, the formula is
=normalcdf(120.5, 99999, 100, (800/9)^0.5)
Using Excel, the formula is
=1-NORMDIST(120.5,100,(800/9)^0.5,TRUE)
The result is 
c) The expected winning is =0.1*1000+0.2*100+0.7*10 = $
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