Students take two independent tests. 30% of the students pass the test A and 60%pass the test B. Find the probability that a student selected at random will pass(a) both tests, (b) only one test.
Question
Students take two independent tests. 30% of the students pass the test A and 60%pass the test B. Find the probability that a student selected at random will pass(a) both tests, (b) only one test.
Solution
(a) Since the two tests are independent, the probability of a student passing both tests is the product of the individual probabilities. So, the probability of passing both tests is 0.30 (probability of passing test A) * 0.60 (probability of passing test B) = 0.18 or 18%.
(b) The probability of passing only one test is the sum of the probabilities of passing test A and not test B, and passing test B and not test A.
The probability of passing test A and not test B is 0.30 (probability of passing test A) * 0.40 (probability of not passing test B) = 0.12 or 12%.
The probability of passing test B and not test A is 0.60 (probability of passing test B) * 0.70 (probability of not passing test A) = 0.42 or 42%.
So, the probability of passing only one test is 0.12 + 0.42 = 0.54 or 54%.
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