A box has four cards numbered 1,2,3, and 4. Yoko will toss a coin once and record the toss as heads (H) or tails (T). Then she will randomly pick a card from the box and record the number chosen. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the coin toss is tails. Use the format H 1 to mean that the coin toss is heads and the number chosen is 1. If there is more than one element in the set, separate them with commas. Sample space: Event that the coin toss is tails:

## Step 1<br />The problem involves two independent events: the coin toss and the card draw. The coin toss can result in either heads (H) or tails (T), and the card draw can result in any of the four numbers: 1, 2, 3, or 4. <br /><br />## Step 2<br />The sample space is the set of all possible outcomes of the experiment. In this case, the experiment involves two independent events: the coin toss and the card draw. The coin toss can result in either heads (H) or tails (T), and the card draw can result in any of the four numbers: 1, 2, 3, or 4. <br /><br />## Step 3<br />The event that the coin toss is tails means that the outcome of the coin toss is T. The card draw can still result in any of the four numbers: 1, 2, 3, or 4. Therefore, the outcomes for this event are T1, T2, T3, and T4.