Bob and Tim have a 2000 Ford Taurus. Every time they drive it, the car breaks down with probability 1/10.
What is the probability that the car breaks down at most one time in the first 50 drives? Compute the probability using Binomial Distribution and also approximate it using a Poisson distribution. Justify the approximation and compare the results.
I've solved this equation using a Binomial Distribution.
My solution: ${50 \choose 1} 0.1^1 (0.9)^{49} = 2.86$%
Now how the hecksies do I approximate this using Poisson Distribution? For instance, I have no idea what $\lambda$ would be because there's no rate lol
First, note that the question is asking about at most one time. Hence you should compute $P(X \le 1)$ rather than $P(X=1)$.
To use Poisson distribution, estimate $\lambda$ as $np$. That is choose it to share the same mean as the binomial distribution.