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Chapter 4: Q.4.61 (page 167)

The probability of being dealt a full house in a hand of poker is approximately .0014. Find an approximation for the probability that in 1000 hands of poker, you will be dealt at least 2 full houses.

Short Answer

Expert verified

An approximation for the probability that in 1000hands of poker, we will be dealt at least 2full houses is 0.408.

Step by step solution

01

Given information

We are given that we have n=1000autonomous Hands of poker, wherein every one of them we have p=0.0014probability to get a Whole House.

02

Calculation

So on intermediate, we will hold λ=np=1.4Full Houses in this session. Hence, we can use the Poisson approximation to get the demand.

So, let Y~Pois(λ).

We have that

P(Y≥2)=1-P(Y=0)-P(Y=1)=1-e-λ-λe-λ≈0.408

03

Final answer

So there is approximately 0.408 probability to get at least two full houses in 1000 hands.

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Most popular questions from this chapter

A certain typing agency employs 2typists. The average number of errors per article is 3when typed by the first typist and 4.2when typed by the second. If your article is equally likely to be typed by either typist, approximate the probability that it will have no errors.

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