Question

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

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

Step-by-step solution

Given information

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

Calculation

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

So, let $Y~Pois\left(\lambda \right)$.

We have that

$P(Y\ge 2)=1-P(Y=0)-P(Y=1)=1-e^{-\lambda }-\lambda e^{-\lambda }\approx 0.408$

Final answer

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