Hey guys,
Im a noob im taking Prob & Stats for Eng. Im only familiar with probability of getting a 4 by rolling a die. Anyway I just wanted to run across some questions by you guys to see if I am approaching them right.
1. Let A denote the event that the next item checked out at a college library is a math book, and let B be the event that the next item checked out is a history book. Suppose that P(A) = .40 and P(B) = .50.
a. Why is it not the case that P(A) + P(B) = 1? My answer: Because there may be other books that can be checked out. ( I was thinking mutually exclusive or independent events but I dont think it applies to the probability not equaling 1)
b. Calculate P(A') My answer: 1-P(A)= 1-.4= .6
c. Calculate P(A U B). My answer: They are mutually exclusive so P(A & B)=0 and P(A U B)= P(A)+P(B)-P(A & B)= .4+.5 -0= .9
2. A real estate agent is showing homes to a prospective buyer. There are ten homes in the desired price range listed in the area. The buyer has time to visit only four of them.
a. In how many ways could the four homes be chosen if the order of visiting is considered? My answer: Order matters so permutation so 10!/(10-4)!= 5040 (This seems wrong to me)
b. In how many ways could the four homes be chosen if the order is disregarded? My answer: Neglecting order so it is combination 10!/4!(10-4)!= 420
c. If four of the homes are new and six have previously been occupied and if the four homes to visit are randomly chosen, what is the probability that all four are new? (The same answer results regardless of whether order is considered.) My answer: Ordered 4!/0!= 4! so 4!/(10!/6!)= (6!*4!)/10! unordered 4!/4!(0!)= 1 so 1/(10!/4!6!)= 4!6!/10! they are the same but how do I actually get the probability?
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