Question

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

Answer 1

It is given that a dice is rolled and then a coin is tossed once if the number comes out to be even and it is tossed twice if the number of die comes out to be odd.

If the dice shows an even number, a coin is tossed once. If the dice shows an odd number, the coin is tossed twice, with sample space { HH,HT,TH,TT }

Thus, the sample space for this experimentis,

S={ 2H,2T,4H,4T,6H,6T,1HH,1HT,1TH,1TT,3HH, 3HT,3TH,3TT,5HH,5HT,5TH,5TT }