Question

Consider all seven-digit numbers that can be created from the digits 0-9 where the first and last digits must be even and no digit can repeat. Assume that numbers can start with 0. What is the probability of choosing a random number that starts with 4 from this group

Answer 1

Answer:

$P_4= 0.2$

Step-by-step explanation:

From the question we are told that

Consider all seven-digit numbers

Created from the digits 0-9

Generally number of digits that starts with 6 is mathematically  given as

The total amount of digits from 0-9(0,1,2,3,4,5,6,7,8,9 = 10

The total amount of even digits within 0-9 (0,2,4,6,8) = 5

The total amount of 3-digit numbers giving the first and last digits to be even = 5 * 10 * 5 = 250

The total 3-digit numbers giving the first digit is 4 and last digit is even = 1 * 10 * 5 = 50

Probability the number starts with 4

      $P_4 = \frac{50}{250}$

      $P_4= 0.2$