Question

A lock is opened when we enter a two digit key. The first digit of the key is a multiple of 5 from 1 through 101 and the second digit is a prime number from 0 through 20. The probability of finding the key through the $\text{above condition is given as}\frac{1}{A}.\text{What is the value}$ of 'A'?

• A. 160

Answer 1

The correct option is A 160
The key is a 2 digit number.

Given, the first digit is a number of multiple of 5 from 1 through 101.

The multiples of 5 are - 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 and 100.

So, the first digit can be chosen from 1 through 100 in 20 different ways.

Now, the second digit (a prime number) can be chosen from 0 through 20 prime numbers in 8 ways - 2, 3, 5, 7, 11, 13, 17 and 19.

∴ The total number of outcomes is
$=20\times 8=160$

Only one time, we can ge the key correct.

So, the probability of getting the correct key
$=\text{P}=\frac{1}{160}=\frac{1}{A}$

Therefore, value of 'A' = 160