Question

A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?

a) {H1, H2, H3, H4, H5, H6}
b) {H2, H4, H6}
c) {H, H2, H4, H6}
d) {H, T}

Answer 1

The sample space for the experiment is {H2, H4, H6}.

Step-by-step explanation:

The sample space for the experiment can be determined by considering the possible outcomes at each step. We start with the first step of flipping the coin, which has two possible outcomes: heads (H) or tails (T). If the outcome is heads, we move on to the next step of throwing the die.

If the die shows up an even number, we throw the die again. There are three possible outcomes for the second throw: 2, 4, or 6.

Putting these outcomes together, the sample space for the entire experiment is {H2, H4, H6}.