Question

consider the experiment of tossing a coin until two heads or two tails appear in succession describe sample space​

Answer 1

The sample space for an event is a collection of all possible outcomes. Therefore, we can say the sample space for rolling a die would be {1,2,3,4,5,6}. Similarly, the sample space for tossing a coin would be {H,T}.

Coming to the event of tossing a coin twice, the first toss would yeild either a H or a T, where H and T belong to the sample space {H,T} as mentioned earlier.

Now coming to the second toss. Suppose the first toss yeilds a H. The second toss can yeild either a H or a T since it once again deals with the sample space of tossing a single coin. Therefore the possible outcomes would be {HH,HT}

Similarly, if the first toss yeilds a T, the second toss would yeild a H or a T and would result in {TH,TT} as outcomes.

Therefore, combining the possibility of the first toss yeilding a H or a T and the second toss subsequently yeilding a H or a T, we have a sample space {HH,HT,TH,TT} for tossing a coin twice.

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