ACT Preparation / Unit 15 ACT 1424 worked example, 60 to 90 seconds
The Chance of At Least One
The idea
An at-least-one probability is found fastest through its complement, in three steps. First, name the opposite event: at least one success is the opposite of no successes. Second, find the probability of no successes, multiplying the chance of failure across independent trials. Third, subtract that from 1.
In practice
Worked example: a free-throw shooter makes 70% of shots, independently. What is the chance of making at least one of three? A miss has probability 0.3, so missing all three has probability 0.3³ = 0.027. At least one make: 1 − 0.027 = 0.973. Second: in four rolls of a die, the chance of at least one 6 is 1 − (5/6)⁴, about 0.52.
Where people slip
Adding the chances, 0.7 + 0.7 + 0.7 = 2.1, gives a probability above 1, which signals the error: the events overlap.
Your place on the trail
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Builds on
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