Self-referencial hint.

Probability Level 4

You are working hard on a probability question, but have no clue on how to solve it. Your friend who has already found the answer provides you with the following accurate hint:

The answer to that question is the probability that the answer is 1.

You are now left with $N$ possible answers to that question, just from your friend's hint. Assuming you pick one of the $N$ answers randomly, the probability that your answer is correct can be expressed as $\frac{a}{b}$ where $a$ and $b$ are coprime positive integers. Find $a + b$ .

The answer is 3.

2 solutions

Muh. Amin Widyatama
Jan 7, 2014

The hint is so accurate:

The answer to that question is the probability that the answer is 1.

We know that a probability of an event has two possible outcome, $1$ or $0$ . One means the event must happen, and zero means the event must not happen. This gives $\frac{1}{2}$ as the probability we consider initially. And finally the answer is $1+2=3$

Sean Elliott
Jan 24, 2014

Once an answer has been determined, the probability that the answer is $1$ is also determined, so it must be either $1$ or $0$ . Thus, the answer can only be $1$ or $0$ .

Note that if the answer is $1$ , then it is $1$ with probability $1$ , and if it is $0$ , then it is $1$ with probability $0$ . So, both $0$ and $1$ check as possible answers.

So the probability of choosing the correct one is $\frac{1}{2}\Rightarrow1+2=\boxed{3}$

Self-referencial hint.

The answer is 3.

2 solutions

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