Question

A super has a key ring with 12 keys. He has forgotten which one opens the apartment he needs to enter. What is the probability he is able to enter before reaching the 4th key?

Answer 1

Therefore, the probability is P=1/4.

Explanation:

We know that a super has a key ring with 12 keys. He has forgotten which one opens the apartment he needs to enter.

We conclude that each key has an equal probability of opening an apartment. Since there are 12 keys, it follows that the probability for each key is equal,

p = 1/12.

We calculate the probability he is able to enter before reaching the 4th key. So he will try three keys by then. We get:

`P=p+p+p\\\\P=(1)/(12)+(1)/(12)+(1)/(12)\\\\P=(3)/(12)\\\\P=(1)/(4)`

Therefore, the probability is P=1/4.