Question

the diagram below shows the sample space for tossing a coin.
tree diagram: first branch head/tails; under head: heads (branches head/tails), tails (branches head/tails); under tails: heads (branches head/tails), tails (branches head/tails)
which three statements about the sample space are true?

• there are three outcomes that have at least three tails.
• one outcome is heads, tails, heads.
• the coin was tossed three times.
• there are 8 possible outcomes.
• you are more likely to toss heads rather than tails.
• there are more outcomes that include heads than tails.

Explanation:

1. "One outcome is Heads, Tails, Heads": By tracing the tree, we can see a path: Head -> Tails -> Head, so this is true.
2. "The coin was tossed three times": The tree has three levels (first toss, second, third), so it's 3 tosses, true.
3. "There are 8 possible outcomes": For 3 tosses, each with 2 options, total outcomes are \(2\times2\times2 = 8\), true.

• "There are three outcomes that have at least three Tails": With 3 tosses, max Tails is 3 (TTT), only 1 outcome, so false.
• "You are more likely to toss Heads rather than Tails": Probability of H and T in a fair coin is equal, false.
• "There are more outcomes that include Heads than Tails": Outcomes with Heads: 7 (all except TTT), outcomes with Tails: 7 (all except HHH), so equal, false.

Answer:

• One outcome is Heads, Tails, Heads.
• The coin was tossed three times.
• There are 8 possible outcomes.