Solution Found!
Poisson Approximation to Binomial Assume that we plan to play the Texas Pick 3 lottery
Chapter 5, Problem 4(choose chapter or problem)
Poisson Approximation to Binomial Assume that we plan to play the Texas Pick 3 lottery 100 times. For one bet, there is a 1/1000 probability of winning. If we want to use the Poisson distribution as an approximation to the binomial, are the requirements satisfied? If we use the Poisson distribution to find the probability of 101 wins, we get an extremely small positive number, so is it correct to conclude that the probability of 101 wins is possible, but highly unlikely?
Questions & Answers
QUESTION:
Poisson Approximation to Binomial Assume that we plan to play the Texas Pick 3 lottery 100 times. For one bet, there is a 1/1000 probability of winning. If we want to use the Poisson distribution as an approximation to the binomial, are the requirements satisfied? If we use the Poisson distribution to find the probability of 101 wins, we get an extremely small positive number, so is it correct to conclude that the probability of 101 wins is possible, but highly unlikely?
ANSWER:
Step 1 of 3:
Poisson distribution:
Poisson distribution is applied to certain discrete cases where the two events are independent of each other, rate of events are constant and two events cannot occur at the same time. The formula for distribution is as follows:
\(P(x)=\frac{e^{-\lambda} \lambda^{x}}{x}\)
If n is the number of attempts, p is the probability of success of a event, then for poisson distribution these two criterias are used:
\(n 100\) ....(1)
\(n p \leq 10\) ....(2)