ACT Math · Probability and counting

A fair coin is flipped 3 times. What is the probability of getting at least one head?

A fair coin is flipped 3 times. What is the probability of getting at least one head?

Answer and explanation

Answer: H: 7/8

Use the complement: the only way to get no heads is three tails, which has probability (12)3=18\left(\frac{1}{2}\right)^3=\frac{1}{8}. So P(at least one head)=1−18=78P(\text{at least one head})=1-\frac{1}{8}=\frac{7}{8}, choice H. Listing the 88 equally likely outcomes shows that only TTT has no heads, so 77 of 88 outcomes qualify. Choice F (18\frac{1}{8}) is the probability of no heads. Choice G (38\frac{3}{8}) is the probability of exactly one head. Choice J (12\frac{1}{2}) is the probability of a head on a single flip.

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