A binomial experiment has a fixed number of independent trials and
only two possible outcomes. Recall that the binomial distribution with parameters n, p, and r gives the probability distribution of the number of r successes in a sequence of n trials, each of which yields success with probability p.
Since there are 5 women having coffee together, the number of trials is fixed at 5. Whether or not one woman likes her mother-in-law will not influence whether or not another woman does, so the trials are
. Finally, there are two possible outcomes: that a woman likes her mother-in-law, or she doesn't. So, this scenario is a binomial experiment with n = 5 trials.
Here we will let a "success" be a woman disliking her mother-in-law. We are given that the probability that a woman does not like her mother-in-law is 90%, so p =..... .
We are interested in the probability that all five women dislike their mother-in-law. Therefore, we want to find the probability of five successes, or P(r =.....) .