Question

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

Answer 1

It is given that a coin is tossed and then a dice is rolled once only in case a tail is shown on the coin. The coin is tossed again if a head occurs.

If a head occurs, coin is tossed again with possibility of getting another head, or a tail.

If a tail occurs, the dice is thrown with possibilities 1, 2, 3, 4, 5, 6.

Thus, the sample space for the experiment is,

S={ HT,HH,( T1 ),( T2 ),( T3 ),( T4 ),( T5 ),( T6 ) }