Question

Writing  Use a word or phrase to describe the likelihood of the statement below. Use pencil and paper. Write similar statements for the same situation that have different likelihoods. Explain why you believe the likelihoods are what you claim.
You flip a fair coin and get a head or a tail.
Question content area bottom
Part 1
What best describes the likelihood of the​ statement?
Impossible
Impossible
Certain
Certain
Likely
Likely
As likely as not
As likely as not
What best describes the likelihood of the statement?

Answer 1

Best descriptor for the statement "You flip a fair coin and get a head or a tail.": Certain.
Explanation: the sample space for one fair coin flip is {H, T}, so probability = 1.

Other similar statements (same coin-flip situation) with different likelihoods:

- Impossible: "You flip the coin once and get both a head and a tail on that single flip."
Why: one flip cannot produce both outcomes, so probability = 0.

- As likely as not: "You flip the coin once and get a head."
Why: P(head) = 1/2 = 0.5, so it is as likely as not.

- Likely: "You flip the coin twice and get at least one head."
Why: P(at least one head) = 1 − P(no heads) = 1 − (1/2)^2 = 3/4 = 0.75, which is greater than 1/2 so it's likely.

(You can check each probability with pencil and paper by listing outcomes or using complementary probability.)