The question is, "Consider the type of clothes dryer (gas or electric) purchased by each of five different customers at a certain store. (a).If the probability that at most one of these purchases an electric dryer is .428, what is the probability that at least two purchase an electric dryer? (b).If P(all five purchase gas)=.116 and P(all five purchase electric)=.005, what is the probability that at least one of each type is purchased?
I am not certain how to answer either question. For (a), we know that P(1 purchases electric)=.428, but does this allow us to infer anything about P(4 purchasing gas)=? Also, would knowing the complement of "1 purchases electric" help at all? What would the complement be? Would it be that no one purchases an electric dryer?
Best Answer
Each of the answers is obtained from the fact that the probability of the event in question the the complement of the given event. So in a), "at most one" is the complement of "at least two". So the prob. Of "at least two" is equal to $1-$ the prob of "at most one". Same reasoning goes for b): "at least one of each" is the prob of "all of one type". Here you have to add both possibilities given.