Correct By Random Chance
Chris finds the following questionnaire in a test:
If you pick your answer randomly between the following choices, what is the probability your answer will be correct?
A. Less than 25%
B. Less than 50%
C. Less than 75%
D. Less than 100%
What is the probability that a random answer in the question above will be correct?
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1 solution
If the desired probability can be determined, there are 0,1,2,3 or 4 correct answers out of 4. This means the possible probabilities of answering correct are 0%, 25%, 50%, 75% and 100%, respectively.
If the probability is 0%, there are four choices (0%<25% ; 0%<50% ; 0%<75% ; 0%<100%) out of four that satisfy that fact. This would however mean that the probability is 100% which contradicts the original assumption (0%).
If the probability is 25%, there are three choices (25%<50% ; 25%<75% ; 25%<100%) out of four that satisfy that fact. This would however mean that the probability is 75% which contradicts the original assumption (25%).
If the probability is 50%, there are two choices (50%<75% ; 50%<100%) out of four that satisfy that fact. Two choices is 50% of four, and the original assumption (50%) is satisfied.
If the probability is 75%, there is one choice (75%<100%) out of four that satisfies that fact. This would however mean that the probability is 25% which contradicts the original assumption (75%).
If the probability is 100%, there are zero choices that satisfy that fact. This would mean that the probability is 0% which contradicts the original assumption (100%).
Therefore, the only possible probability of answering correct is 5 0 %.