Final answer:
The tree diagram represents the sample space of spinning the spinner and flipping the coin. Out of 8 possible outcomes, only 2 satisfy the condition of spinning a 3 or a 4 and flipping a head. Therefore, the probability is 1/4.
Step-by-step explanation:
To represent the sample space of spinning the spinner and flipping the coin, we can create a tree diagram. The branches of the tree represent the possible outcomes of each action. In this case, the spinner has four equal sections numbered 1-4, and the coin has two sides - heads and tails.
The tree diagram would start with the spinner and have four branches representing the numbers 1, 2, 3, and 4. Each of these branches would then have two branches representing the coin toss - one for heads and one for tails.
Therefore, the sample space would consist of 8 possible outcomes: 1H, 1T, 2H, 2T, 3H, 3T, 4H, and 4T.
Out of these 8 outcomes, only two of them satisfy the condition of spinning a 3 or a 4 and flipping a head, which are 3H and 4H. Therefore, the probability of spinning either a 3 or a 4 AND flipping a head is 2/8 or 1/4.