Question

An experiment consists of rolling a die and then tossing a coin once it 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

Given: A dice is rolled and then a coin is tossed once. 

To Find: Write the sample space for the given experiment. 

Explanation: A dice has 6 faces that are numbered from 1 to 6. 

And, we know, 2, 4, 6 are even numbers and 1, 3, 5 are odd numbers. 

Now, A coin has two face, Head(H) and Tail(T) 

So, we can find the total sample spaces by combining both experiments as 

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

Hence, S is the required sample space for given experiment.