In a multiple choice question paper with four options, getting the answer right with the first guess (that is, if we don't know the answer) has a probability of $\frac{1}{4}$. What are are the probabilities for getting the correct answer on the second, third or fourth guesses?

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### Solution

The probability of getting it right on the first guess is ¼ as already stated. On second guess it's $\frac{3}{4}\times \frac{1}{3}=\frac{1}{4}$ so the same. For the third guess, $\frac{3}{4}\times \frac{2}{3}\times \frac{1}{2}=\frac{1}{4}$ so same again and the forth isn't a guess as it's the last one remaining with a probability of, you guessed it, $\frac{1}{4}$.

So guessing wrong doesn't improve your chance of guessing right at any point.

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