Please help me. the sample space, S. Try to compute |S|, the size of S, and expl

Question

Please help me.

the sample space, S. Try to compute |S|, the size of S, and explainyour reasoning. A. Three people enterthe elevator in the basement of a building with 6 floors. Eachstates
where he will get out. B. A box has 10 chips.The rst is numbered with a "1", the second with a "2", etc. A chipis
drawn from the box, its value noted, and then it is returned to thebox. Then a second chip is
drawn and its value noted. C. As in (B) but thechips are NOT returned to the box. Please help me.

the sample space, S. Try to compute |S|, the size of S, and explainyour reasoning. A. Three people enterthe elevator in the basement of a building with 6 floors. Eachstates
where he will get out. B. A box has 10 chips.The rst is numbered with a "1", the second with a "2", etc. A chipis
drawn from the box, its value noted, and then it is returned to thebox. Then a second chip is
drawn and its value noted. C. As in (B) but thechips are NOT returned to the box.

Explanation / Answer

A. (6) x (6) x (6) = 216    Thereare 3 people so there are 3 "boxes" to fill. We're assumingthat each person's choice of                                          floor is independent of the other people.They each can pick any one of 6 floors.                                          The outcome could be floor 1, floor 1, floor 1; orfloor 1, floor 1, floor 2; or floor 1, floor1,                                           floor3 . . There are 216 different possible outcomes. Note thatperson 1 to floor 3 and person                                          2 to floor 5 is a different outcome than person 1 to floor 5and person 2 to floor 3. B. (10) x (10) =100           Twochips will be drawn so there are two "boxes" to fill. Thereare 10 different values.                                           Because the first chip picked is returned(with replacement), it can be selected thesecond                                           time as well. The possible value of the secondchip is not dependent on (changed by) the                                           value of the first chip. There are still 10 differentvalues. It's independent. C. (10) x (9 ) =90              Two chips will be drawn so there are two "boxes" to fill. There are 10 different values.                                            Because the first chip is not returned (withoutreplacement), it can't be selected the second                                             timeas well. The possible value of the second chip isdependent on (changed by) the value                                            of the first chip. Now there are only 9 different possiblevalues.

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