1983 AHSME Problems/Problem 26
Problem
The probability that event occurs is ; the probability that event B occurs is . Let be the probability that both and occur. The smallest interval necessarily containing is the interval
Solution
Firstly note that and , as clearly the probability that both and occur cannot be more than the probability that or alone occurs. The more restrictive condition is , since .
Now, by the Inclusion-Exclusion Principle, we also have and as a probability must be non-negative, , so . Therefore, combining our inequalities gives , which is answer choice .
See Also
1983 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 25 |
Followed by Problem 27 | |
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