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 two will be Acers.
Write your answers in exact, simplified form.
Part 1 of 3
(a) The probability that all three will be Acers is 0.125 .
Part: $1 / 3$
Part 2 of 3
(b) The probability that exactly two will be Dells is $0.45^{\infty}$.
Answer
For part (b), we need to find the probability that exactly two of the computers chosen are Dells. This is a bit more complicated, as it involves combinations. We need to consider the different ways we can choose two Dells out of three choices, and multiply this by the probability of choosing a Dell (0.5) raised to the power of 2 (since we want two Dells), and the probability of choosing an Acer (0.5) raised to the power of 1 (since we want one Acer). The probability that exactly two of the computers chosen will be Dells is \(\boxed{0.375}\).
Step 1 ：The problem is asking for the probability of certain outcomes when choosing three computers from an inventory of Dell and Acer computers, assuming there are equal numbers of each brand.
Step 2 ：For part (a), we need to find the probability that all three computers chosen are Acers. Since there are equal numbers of each brand, 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 computers chosen will be Acers is \(\boxed{0.125}\).
Step 3 ：For part (b), we need to find the probability that exactly two of the computers chosen are Dells. This is a bit more complicated, as it involves combinations. We need to consider the different ways we can choose two Dells out of three choices, and multiply this by the probability of choosing a Dell (0.5) raised to the power of 2 (since we want two Dells), and the probability of choosing an Acer (0.5) raised to the power of 1 (since we want one Acer). The probability that exactly two of the computers chosen will be Dells is \(\boxed{0.375}\).
