Problem

Three computers are chosen at random from an Inventory of Dell and Acer computers for a bookstore display. Assume the same number each brand of computers is in stock. Find the prbability that (a) All three will be Acers. (b) Exactly two will be Dells. (c) At most one will be Acer. Write your answers in exact, simplified form. Part 1 of 3 (a) The probability that all three will be Acers is $\frac{1}{8}$. Part 2 of 3 (b) The probability that exactly two will be Dells is 0.375 . Part: $2 / 3$ Part 3 of 3 (c) The probability that at most one will be Acer is

Solution

Step 1 :For part (a), we need to calculate the probability that all three computers chosen are Acers. Since we are assuming that the number of Dell and Acer computers in stock is the same, the probability of choosing an Acer for any given choice is 0.5 (or 1/2). Since we are choosing three computers, and we want all of them to be Acers, we need to multiply the probabilities together. The probability that all three will be Acers is \(\boxed{0.125}\).

Step 2 :For part (b), we need to calculate the probability that exactly two of the computers chosen are Dells. This is a bit more complicated, because we need to account for the different ways that two Dells and one Acer could be chosen. The probability that exactly two will be Dells is \(\boxed{0.375}\).

Step 3 :For part (c), we need to calculate the probability that at most one of the computers chosen is an Acer. This means we need to calculate the probability that none of the computers are Acers, and the probability that exactly one of the computers is an Acer, and then add these probabilities together. The probability that at most one will be Acer is \(\boxed{0.5}\).

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Source: https://solvelyapp.com/problems/15680/

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