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Q #5 The computers of six faculty members in a certain department are to be replaced....

Q #5 The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that only two of the setups can be done on a particular day, and the two computers to be set up are randomly selected from the six (implying 15 equally likely outcomes; if the computers are numbered 1, 2,…, 6, then one outcome consists of computers 1 and 2, another consists of computers 1 and 3, and so on).

a. What is the probability that both selected setups are for laptop computers?

b. What is the probability that both selected setups are desktop machines?

c. What is the probability that at least one selected setup is for a desktop computer?

d. What is the probability that at least one computer of each type is chosen for setup?

Expert Solution

Given: There are total 6 computers faculty members.

2 of them are selected laptops and 4 of them are selected desktop

2 computers are selected from 6 that is

There are total 15 equally likely outcomes of selecting two computers.

a. P(both selected setups are for laptop computers)

That is select 2 from 2 laptops and the total are 15 possibilities.

Or we can take the probability as,

Therefore, the probability that both selected setups are for laptop computers is 1/15

b. The probability that both selected setups are desktop machines.

That has to select both desktops from 4.

Therefore, the probability that both selected setups are desktop machines is 6/15.

c. The probability that at least one selected setup is for a desktop computer.

At least one desktop means either one is desktop or both are a desktop.

There are 3 possibilities either first is desktop and second is a laptop OR first laptop and second desktop OR both are desktops.

Therefore, the probability that at least one selected setup is for a desktop computer is 14/15

d. The probability that at least one computer of each type is chosen for setup.

Only 2 have to select, so at least one of each type means both are selected that is either laptop then desktop OR desktop then a laptop.

Therefore, the probability that at least one computer of each type is chosen for setup is 8/15.

milcah answered 11 months ago

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