Question

There are 100 boards in a box on which the number 1 to 100 is 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

First of all, we will calculate the total number of possible outcomes. There are 100 possible outcomes. Now, find the number of favourable outcomes for each condition. Further, use the formula $\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of possible outcomes}}}}$ to calculate the desired probability.

Complete step by step answer:
There is a total of 100 boards.
In part (1) we have to find the probability of selecting the number on board with a two-digit number.
We know that the two-digit numbers from 1 to 100 are 11,12,13……….99.
There are 90 numbers with two-digit numbers on the board.
The formula for the probability is $\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of possible outcomes}}}}$
Then, the probability of two-digit number is $\dfrac{{90}}{{100}} = \dfrac{9}{{10}}$
In part (2), we have to find the probability of selecting a number which is a multiple of 7.
The multiples of 7 from 1 to 100 are 7,14,21,………98.
We will now find the number of multiples of 7 from 1 to 100 by dividing 98 by 7.
Hence, there are $\dfrac{{98}}{7} = 14$ numbers.
Then, the probability of selecting a board with number 7 is $\dfrac{{14}}{{100}}$
On simplifying we get the probability as $\dfrac{7}{{50}}$
In part (3), we have to find the probability of selecting the number onboard which is a four-digit number.
As we know, there is no four-digit number from 1 to 100.
Thus, the probability of the four-digit number is 0.

Note: The probability of any event can never be negative. Also, the probability of an event cannot be greater than 1. The event with 0 as the probability is known as an impossible event. And, the event with a probability as 1, is known as a sure event.