Which of these situations could be modelled using the binomial distribution?
For those which can be modelled by the binomial distribution $\mathrm{B}(n,p)$, what are "success" and "failure", and what are $n$ and $p$?
For those which are not, why not? Is there something small you could change that would make the binomial distribution appropriate? Is the binomial distribution at least a good approximation in this situation?
A bag contains red, green and blue balls. 10 balls are taken at random, one at a time. Each ball's colour is recorded, and then returned to the bag.
A coin is flipped until a tail is obtained. The total number of flips needed is recorded.
The number of rainy days in April in the village of Springfield is recorded.
The children in a class each do the same mathematics test. The number who score above 80% is recorded.
Five fair coins are stuck to a piece of clear plastic. The plastic is flipped in the air, and the number of heads showing when the plastic lands is recorded.
A person plays a lottery every week. They record the number of times they win a prize during one year.
A cancer drug is being tested. 1000 patients are given the drug, and the number of patients who die within five years is recorded.
A basketball player is practising taking shots. The number of successful shots out of 10 attempts is recorded.
A bag contains red and blue balls. 10 balls are taken at random, one at a time. Each ball's colour is recorded, and then returned to the bag.
A box of pens contains working pens and broken pens. 10 pens are taken together from the box at random, and the number of working pens is recorded.
A bag contains red, green and blue balls. 10 balls are taken from the bag at random one at a time, and replaced immediately. The number of green balls taken is recorded.
A farmer is planting a crop. On average, a certain percentage of the seeds grow to maturity. The number of seeds that grow to maturity in this field in this year is recorded.