Dear Door code

In a situation of equiprobability we count the eventualities that make up the universe or the events to study for that we can either use the combinations when the random experience allows it or count trees and diagram which allows to model the proposed experience.

To access a house you must enter a code of 2 letters and three digits from 0 to 9 : the code consists of a letter followed by a list of 3 digits which are not necessarily distinct. The letters are A and B.

1. Work out the number of possible codes.

2. What is the probability that a visitor opens the door on the first try when he or she has entered a code completely at random?

You have to create a tree diagram to count all the possible cases.

1. There are 2000 possible codes. There is only one correct code out of the 2000 possible.

2. The probability of entering the correct code is 1/2000.