ITPEC FE Morning April 2023 Question 3
Topic: Basic Theory
What is the probability that at least three coins land heads up when four unbiased coins are tossed simultaneously?
Explanation
5/16 — count the outcomes with three or four heads among the 16 equally likely outcomes.
- •All outcomes: 24 = 16
- •Exactly three heads: C(4, 3) = 4
- •Exactly four heads: C(4, 4) = 1
- •Probability: (4 + 1) ÷ 16 = 5 ÷ 16
Answer (b)
Why not others:
- •(a) 1/4 — 4/16 counts only exactly three heads and misses the all-heads outcome
- •(c) 3/8 — 6/16 is the probability of exactly two heads
- •(d) 5/8 — 10/16 is the chance that at least three coins show the same face, heads or tails, so it counts the tails case as well
Key rule: "At least k" means adding the cases k, k + 1, …, n, or subtracting the complementary cases from 1 when there are fewer of them.
Basic Theory · AI-written, may contain errors
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