Hat # 1 contains one gold coin, one silver coin and one copper coin. Hat # 2 con

Question

Hat # 1 contains one gold coin, one silver coin and one copper coin. Hat # 2 contains two gold coins and two silver coins.

For each of the following experiments, give the complete sample space of outcomes.

(a) You randomly select one coin from each hat. The outcome of interest is the colour of each of the selected coins.

(b) You randomly select two coins from Hat # 1 without replacement. The outcome of interest is the colour of each of the selected coins.

(c) You repeatedly select coins from Hat # 1, without replacement, until the gold coin is selected. The outcome of interest is the colour of each of the coins selected during this process.

(d) You repeatedly select coins from Hat # 2, without replacement, until both gold coins are selected. The outcome of interest is the colour of each of the coins selected during this process.

Explanation / Answer

Let us denote the gold coin by G,silver coin by S and copper coin by C.

Then,

(a) Sample space={GG,GS,SS,SG,CG,CS}

(b) Sample space={GS,SG,GC,CG,SC,CS}

(c) Sample space={G,SG,CG,SCG,CSG,SCG}

(d) Sample space={GG,SGG,GSG,SSGG,SGSG,GSSG}

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