Question

which two statements are true about the situation? there are more outcomes involving the numbers 1, 2, and 3 than the numbers 4, 5, and 6. you are twice as likely to roll an odd number on the die as roll an even number. you are more likely to land on heads than tails when flipping the coin. the coin has 2 possible outcomes, and the die has 6 possible outcomes. the experiment has a total of 12 outcomes.

Explanation:

1. Analyze "There are more outcomes involving the numbers 1, 2, and 3 than the numbers 4, 5, and 6": For each coin outcome (Head/Tail), numbers 1 - 3 and 4 - 6 each have 3 outcomes. So total for 1 - 3: \(2\times3 = 6\), for 4 - 6: \(2\times3 = 6\). So this is false.
2. Analyze "You are twice as likely to roll an odd number on the die as roll an even number": On a die, odd numbers (1, 3, 5) and even numbers (2, 4, 6) each have 3 outcomes. Probability of odd = \(\frac{3}{6}=\frac{1}{2}\), even = \(\frac{3}{6}=\frac{1}{2}\). Not twice as likely. False.
3. Analyze "You are more likely to land on heads than tails when flipping the coin": A fair coin has equal probability (\(\frac{1}{2}\)) for heads and tails. False.
4. Analyze "The coin has 2 possible outcomes, and the die has 6 possible outcomes": A coin can be Head (H) or Tail (T) – 2 outcomes. A die has 1, 2, 3, 4, 5, 6 – 6 outcomes. True.
5. Analyze "The experiment has a total of 12 outcomes": From the tree, Head has 6 outcomes, Tail has 6 outcomes. Total \(6 + 6 = 12\). True.

Answer:

• The coin has 2 possible outcomes, and the die has 6 possible outcomes.
• The experiment has a total of 12 outcomes.