Question

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 probability that
(a) all three will be dells.
(b) exactly two will be acers.
(c) at most two will be acers.
write your answers in exact, simplified form.
part: 0 / 3
part 1 of 3
(a) the probability that all three will be dells is

Explanation:

Step1: Determine the probability of choosing a Dell computer

Since there are two brands (Dell and Acer) and the same number of each brand, the probability of choosing a Dell computer on the first draw is \(P(D_1)=\frac{1}{2}\).

Step2: Calculate the probability for three - consecutive Dell choices

Since the draws are independent (assuming sampling with replacement or a large inventory), the probability that all three are Dells is \(P = P(D_1)\times P(D_2)\times P(D_3)\). Substituting \(P(D_i)=\frac{1}{2}\) for \(i = 1,2,3\), we get \(P=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\).

Answer:

\(\frac{1}{8}\)