1. ## Probability

If 30% of commuters ride to work on a bus, find the probability that if 8 workers are selected at random, 3 will ride the bus.

There are several questions like this on my assignment and I have had no luck in figuring out how to work them after several hours of looking through class notes and on the internet. If someone could solve this and show how they came to the answer, I would appreciate it very much and hopefully be able to complete the rest of the assignment on my own.

If 30% of commuters ride to work on a bus, find the probability that if 8 workers are selected at random, 3 will ride the bus.

There are several questions like this on my assignment and I have had no luck in figuring out how to work them after several hours of looking through class notes and on the internet. If someone could solve this and show how they came to the answer, I would appreciate it very much and hopefully be able to complete the rest of the assignment on my own.
this is a binomial distribution problem. we have independent trials, each can be classified as a success or failure.

let success be that the person does ride the bus.

so the probability of sucess is 0.3
this means the probability of failure is 0.7
we have 8 trials here and we want 3 successes

so $P(k) = {n \choose k} p^kq^{n - k}$

where $n$ is the number of trials, $p$ is the probability of success, $q$ is the probability of failure, $k$ is the number of success, and $P(k)$ is the probability of $k$ successes

so you want $P(3)$