Question

A four-digit number is to be formed by using the digits. 2, 4, 7, 8. The probability that the number will start with 7 is

Answer 1

We know that

$\text{Probability of an event}=\frac{\text{Number of outcomes}}{\text{Total number of outcomes}}$

Given: Four digits $2,4,7,8$

To find: Probability of the number that will start with $7$

On solving, we get:

$& \text{Probability of an event}=\frac{\text{Number of outcomes}}{\text{Total number of outcomes}} \\ & =\frac{3!}{4!} \\ & =\frac{3\times 2\times 1}{4\times 3\times 2\times 1} \\ & =\frac{1}{4}$

Therefore, the probability that a number will start with $7$ is $\frac{1}{4}$

Answer 2

Using,

Probability of an event $=\frac{Possible \ Outcomes}{Total \ Outcomes}$

Given: Formed a four-digit using the digits 2, 4, 7, 8.

The probability that the number will start with 7 is,

Fix 7 in the thousand places and interchange the position of 2, 4, 8 in one's, ten's, and hundred's places.

Possible outcomes= $3!$

Total 4 digit numbers are formed using the digits 2, 4, 7, and 8.

Total outcomes =$4!$

Probability of an event that the number will start with 7  $=\frac{3!}{4!}$

$=\frac{3!}{4\times 3!}\\=\frac{1}{4}$