For each of the following situations, determine the complete sample space or out

Question

For each of the following situations, determine the complete sample space or outcomes. (a) A student who waits for two buses every day records the status of the arrival of each bus. The bus is either late, on time, or early. The outcome of interest is the status of each bus for one day. (b) Two standard decks of cards (consisting of 13 hearts, 13 diamonds, 13 spades and 13 clubs) is shuffled. One card is randomly selected from each deck. The outcome of interest is the suit that is selected from each deck. (c) There are three coins in a hat - one gold, one silver and one copper. You will randomly select coins without replacement until the gold coin is selected. The outcome of interest is the colour of each coin that is selected during this process.

Explanation / Answer

a)

let L be late

E be early

and OT means on time

the sample space is { (outcome for first bus, outcome for second bus) }

{ (E,E) (L,L) (OT,OT) (E,L) (E,OT) (OT,E) (OT,L) (L,OT) (L,E) }

total 9 outcomes in the sapmle space

b)

let (C)club, (D)diamond, (H)hearts, (S)spades be the four suits .

the sample space is { (suit of card drawn from first deck , suit of card drawn from second deck) }

{ (C,C) (D,D) (H,H) (S,S) (C,H) (C,D) (C,S) (D,C) (D,H) (D,S) ( H,C) (H,D) ( H,S) (S,C) (S,D) (S,H) }

total 16 outcomes

c)

Ley G be the gold coin

S be the silver coin

C be the copper coin

The sample space is

{ (G)(S,G)(C,G)(S,C,G)(C,S,G) }

the sample space has only 5 outcomes as replacement is not allowed and the gold can come as the first drawn coin or the second or the third drawn coin

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