Probability of The Correct Answer?

This is a popular probability puzzle in which you have to select the correct answer at random from the four options below.

Can you tell, whats the probability of choosing correct answer in this random manner.

1) 1/4
2) 1/2
3) 1
4) 1/4

And the correct answer is......

Finding The Probability of Correct Answer

What was the question?

It can't be 1/4 as 1/4 appears 2 times in given 4 options as probability of correct answer when random selection of option in that case would be 2/4 = 1/2. This will be contradiction.

It can't be 1/2 either since the probability of the 1 correct answer out of 4 available options on random selection would be 1/4. That will be contradiction again.

It can't be 1 too as again probability of the 1 correct answer out of 4 available options on random selection would be 1/4. Once again this is contradiction.

Hence, the probability of the 1 correct answer out of 4 available options on random selection would be 0.

Case of 3 Identical Notebooks

Three people all set down their identical notebooks on a table. On the way out, they each randomly pick up one of the notebooks. What is the probability that none of the three people pick up the notebook that they started with?

That's correct probability!

Probability in Case of 3 Identical Notebooks

What was the case?

Let's name peoples as Person - 1, Person - 2, Person - 3 and their notebooks as Notebook - 1, Notebook - 2 and Notebook 3 respectively.

Now there can be 6 ways 3 notebooks can be distributed among 3 persons like below.

(Here, for convenience, 3 different colors are assigned to the notebooks of 3 persons.)

As we can see, there are only 2 cases, where the each of person not getting own notebook. In rest of cases, at least 1 person got own notebook & notebooks of others are shuffled between 2.

So the probability that none of the three people pick up the notebook that they started with is 2/6 = 1/3.