An experiment consists of tossing a coin and then throwing it second times if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

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Solution

A coin is tossed then $S_{1} = {H, T}$
A coin is tossed again then $S_{2} = {H, T}$
A die is rolled then $S_{3} = {1, 2, 3, 4, 5, 6}$
Hence $S = {H H, H T, T 1, T 2, T 3, T 4, T 5, T 6}$

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An experiment consists of tossing a coin and then throwing it second times if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

A coin is tossed then S1={H,T} A coin is tossed again then S2={H,T} A die is rolled then S3={1,2,3,4,5,6} Hence S={HH,HT,T1,T2,T3,T4,T5,T6}

A coin is tossed then $S_{1} = {H, T}$
A coin is tossed again then $S_{2} = {H, T}$
A die is rolled then $S_{3} = {1, 2, 3, 4, 5, 6}$
Hence $S = {H H, H T, T 1, T 2, T 3, T 4, T 5, T 6}$