ITPEC FE Morning April 2023 Question 3

Binomial Probability (at least k successes) — count favorable outcomes using combinations.

"At least 3 heads from 4 fair coins":

• •Total outcomes: 2⁴ = 16
• •Exactly 3 heads: C(4,3) = 4
• •Exactly 4 heads: C(4,4) = 1
• •P(at least 3) = (4 + 1) / 16 = 5/16

Why not others:
- (a) 1/4 — counts only exactly 3 heads (4/16), misses the all-heads case
- (c) 3/8 — 6/16, no valid combination produces this
- (d) 5/8 — 10/16, this would be "at least 2 heads"

Key rule: "At least k" = sum all cases from k to n using C(n, i) / 2ⁿ.

AI-generated — may contain errors