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.

Question

Philoid · Accepted Answer

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.