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Area Man Who Talks a Lot About Teaching Teaches His First Full Day in >10
Years
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I have taught demo and observational classes regularly since I left
full-time teaching but yesterday was the first time I taught every class
for the day. L...
3 years ago
The answer is 1/4.
ReplyDeleteOnce the student has answered the other questions, the parity of his score (odd or even) will depend on his response to the last question. Therefore, his score is even with probability 1/2.
Suppose that the score S is even. If he had reversed all of his responses, writing true for false and false for true, then his score would have been (50 - S), which is also an even number. But note that exactly one of the two quantities S and (50 - S) is a multiple of 4. So, if S is even, then the probability is 1/2 that it is also divisible by 4.
Therefore, the probability that the score is divisible by 4 is 1/2 * 1/2 = 1/4.
REMARK: This argument is valid when the number of questions is congruent to 2 modulo 4. In other cases, the probability would be slightly different than 1/4. It is a challenge to find the exact probability in those cases.