A, B, and C take turns flipping a coin, and suppose A flips first, then B flips,

Question

A, B, and C take turns flipping a coin, and suppose A flips first, then B flips, and then C flips. The process continues until the first one gets a head. In this case, that person wins. The sample space can be defined by Ohm = {1, 01,001,0001, ...,000...(infinitely many 0's)}. Interpret the sample space. That is, you should give a brief English description why Ohm captures the experiment. In particular, what does each element in the sample space mean? Define the following events. (Note that an event is a subset of the sample space). W_A be the event that A wins. Describe what W_A should be. W_B be the event that B wins. (W_A W_B)^c.

Explanation / Answer

1) sample space is combination of events for the process which continues till we get first head.

here in sample space first event {1} is that A flip and receive head on first flip.

{01} represent event represent that A flip and got tail after that B flips and got head.

{001} represent event represent that A flip and got tail after that B flips and got tail and then C flip and got head.

and so on till we get first head.

Wa= {1,0001,0000001,....} is the collection of events (when A flip head , ABC all flip tails then A flip heads,ABC

flip tail again ABC flip tail and then A flip head

2)Wb={01, 00001; 0000001;..}is the collection of events (when A flip tail and B flip Tail ; ABCA all flip tails then B flip heads ;

ABC

flip tail again ABCA flip tail and then B flip head

3)(WaUWb) is the event where either A wins or B wins

hence (WaUWb)c is event where neither A or B wins. Hence it reflect that C wins

hence  (WaUWb)c ={001; 000001 ; 000000001;......}

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