Question

There are $100$ boards in a box on which the number $1$ to $100$ are written. If one board is selected randomly from a box then find the probability of:
(1) The number on the board is two digit.
(2) The number on the board is a multiple of $7$.
(3) The number on the board is four digit.

Answer 1

Total number of outcomes=100

1)

The number of two digit numbers in 1 to 100$=98$ (all numbers except 1 and 100)

Probability that the number on board is two digit$=\frac{\text{Number of two digits numbers in 1 to 100}}{\text{Total number of outcomes}}=\frac{98}{100}=\frac{49}{50}$

2)

The number of multiples of 7 in 1 to 100$=14$ $(7,14,21,28,35,42,49,56,63,70,77,84,91,98)$

Probability that the number on board is two digit$=\frac{\text{Number of multiples of 7 in 1 to 100}}{\text{Total number of outcomes}}=\frac{14}{100}=\frac{7}{50}$

3)

The number of 4-digit numbers$=0$

Probability that the number on board is four digit$=\frac{\text{Number of 4-digit numbers in 1 to 100}}{\text{Total number of outcomes}}=\frac{0}{100}=0$