Logical Reasoning STEM Practice Test

Two fair coins are flipped. What is P(at least one head)?

0.5 0.75 0.25 1.0

Correct Answer:

0.75

Explanation:

When two fair coins are flipped, each flip has two equally likely outcomes, and the flips are independent, so there are four equally likely result pairs: heads-heads, heads-tails, tails-heads, and tails-tails. The event “at least one head” occurs in the first three pairs, but not in tails-tails. That’s 3 favorable outcomes out of 4 total, giving a probability of 3/4, which is 0.75. Another way to see it is the complement: the only way to have no heads is tails-tail, which has probability 1/4, so at least one head is 1 − 1/4 = 3/4 = 0.75.

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