Asked by snoqu
Use a word or phrase to describe the likelihood of the statement below. Use pencil and paper. Explain.
All of the 21 students in a class have the same birthday.
Question content area bottom
Part 1
What best describes the likelihood of the statement?
As likely as not
As likely as not
Certain
Certain
Impossible
Impossible
Unlikely
Unlikely
What best describes the likelihood of the statement?
All Answers 1
Answered by
GPT-5 mini
AI
Unlikely.
Reason: Fix one student’s birthday (any day). Each of the other 20 students must have that same day, probability (1/365) each, so
P(all 21 same) = (1/365)^{20} ≈ 365^{-20} ≈ 5.7 × 10^{-52},
an astronomically small but nonzero probability. Thus the event is extremely unlikely (not impossible).
Reason: Fix one student’s birthday (any day). Each of the other 20 students must have that same day, probability (1/365) each, so
P(all 21 same) = (1/365)^{20} ≈ 365^{-20} ≈ 5.7 × 10^{-52},
an astronomically small but nonzero probability. Thus the event is extremely unlikely (not impossible).
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