Question

A lock is opened when we enter a two digit key. The first digit of the key is an alphabet and the second digit is an even number from 0 through 20. The probability of choosing the key through the above $\text{condition is given as}\frac{1}{A}.\text{What is the value of 'A'?}$

• A. 260

Answer 1

The correct option is A 260
The key of the lock is composed of a 2 digit number.

Given, first digit is an alphabet.
There are 26 alphabets.

So, first digit can be chosen from A through Z in 26 different ways.

The second digit of the key is an even number from 0 through 20. There are 10 even numbers between 0 and 20, starting from 0.

So, the second digit can be chosen in 10 ways.

∴ Total number of outcome will be
$26\times 10=260$

Only one time, we can get the key perfectly correct.

So, the probability of to getting the correct key is
$\text{P}=\frac{1}{260}=\frac{1}{A}$

Therefore, value of 'A' = 260