ACT Math · Probability and counting
A student takes two independent tests. The probability of failing test A is 0.2, and the probability of failing test B is 0.3. What is the…
A student takes two independent tests. The probability of failing test A is 0.2, and the probability of failing test B is 0.3. What is the probability the student passes at least one of the two tests?
Answer and explanation
Answer: H: 0.94
It is easier to use the complement: P(pass at least one) = 1 − P(fail both) = 1 − (0.2)(0.3) = 1 − 0.06 = 0.94. Choice F reports P(fail both) itself instead of its complement. Choice G reports P(pass both tests), 0.8×0.7=0.56, instead of P(pass at least one). Choice J adds the two failure probabilities directly, 0.2+0.3=0.5, which does not correctly combine independent probabilities.
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