1. A $1 scratch off lotto ticket will be a winner one out of 10 times....

1. A $1 scratch off lotto ticket will be a winner one out of 10 times. Out of a shipment of n = 200 lotto tickets, using the Poisson distributions in each case (for a, b and c), find the probability for the lotto tickets that there are: a. somewhere between 75 and 95 prizes. b. somewhere between 15 and 25 prizes. c. more than 50 prizes d.If a customer keeps buying tickets till she finds a winner, find the probability that her 10^th ticket will be a winner.

Solutions

Expert Solution

Let X is a random variable shows the number of prizes out of 200. Here X has binomial distribution with parameters as follow:

Since so we can use Poisson approximation. Using Poisson approximation, X will have Poisson distribution with parameter

The pdf of X will be

(a)

The probability for the lotto tickets that there are somewhere between 75 and 95 prizes is

Excel function used for finding probability is "=POISSON(94,20,TRUE)-POISSON(75,20,TRUE)"

Answer: 0.0000

(b)

The probability for the lotto tickets that there are somewhere between 15 and 25 prizes is

Excel function used for finding probability is "=POISSON(24,20,TRUE)-POISSON(15,20,TRUE)"

Answer: 0.6867

(c)

The probability for the lotto tickets that there are more than 50 prizes is

Excel function used for finding probability is "=1-POISSON(50,20,TRUE)"

Answer: 0.000000004828

(d)

Let Y is a random variable shows the number of tickets need to buy till she finds a winner. Using geometric distribution with parameter p = 0.10 the required probability is

Answer: 0.0387

milcah answered 1 year ago

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