Suppose that typically $\frac3{10}$ of the customers order “grande” mocha. Assume that customers are independent.
a. What is the probability that exactly $2$ of the next $5$ customers will order a “grande” mocha?
b. What is the probability that the $1$st $3$ customers do not order “grande” mochas and the $4$th and $5$th customers do order “grande” mochas?
My work:
a) I used the binomial distribution for this: $P(X=2) = {5 \choose 2}.3^2.7^3 = .3087$
b) I need help with b) I know that the $1$st $3$ customers do not order “grande” mochas and the $4$th and $5$th customers do order “grande” mochas is one specific outcome. But I'm not sure how what the denominator (all total outcomes) would be in order to calculate probability. Can someone give me a clue?
Since the customers are independent, the probability in (b) can be found just by multiplying the probabilities in each slot together. The answer is found by removing the $\binom52$ factor from (a): $.3^2.7^3=0.03087$.