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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?

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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.

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Do you happen to mean that, "at most two," is the complement of "at most one?" Because it doesn't take about "at least one" in part a). If is true, then you are saying that, out of everything that can happen (the sample space, which has a probability of 1), is composed only of the even that at most one person buys an electric dryer and at most two people buy an electric dryer? What about at most three people buy an electric dryer? –  Mack Jan 29 '13 at 14:17
    
Sorry, I meant "at most one" and "at least two" throughout. I will edit. –  Ron Gordon Jan 29 '13 at 14:44
    
let the event $A$ be such that it will contain the outcomes where only one person buys an electric dryer. Then $A = \{egggg, geggg, ggegg, gggeg, gggge\}$, right? So, $P(A)=.428$, right? I ask these questions, because putting things in terms of symbols helps me more often than not. –  Mack Jan 29 '13 at 15:03
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Yes, but remember that the events about which you are asked is "at most one" electric and "at least two" electrics. "At most one" implies zero or one electric dryer; "at least two" implies 2, 3, 4, or 5 electric dryers. Note that these two events cover all possibilities, so the sum of the probabilities of these two cases is 1. Because the prob. of "at most one" is 0.428, then the prob. of "at least two" is... –  Ron Gordon Jan 29 '13 at 15:18
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Again, "at least one of each type" is the complement of ("all gas" or "all electric"). The "or" means add the probabilities because these cases are mutually exclusive. –  Ron Gordon Jan 29 '13 at 16:04
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