Question

Стас выбирает трехзначное число. Найдите вероятность того, что оно делится на 48

Answer 1

Всего трехзначных чисел 999-99=900
Из них чисел кратных 48 восемнадцать
a1=144  d=48
144+48*(n-1)≤999
48(n-1)≤855
n-1≤17 13/16
n≤18 13/16
n=18
Вероятность равна 18/900=0,02

Answer 2

Probability of a Three-Digit Number Divisible by 48

To find the probability that a three-digit number is divisible by 48, we need to determine the number of three-digit multiples of 48 and divide it by the total number of three-digit numbers.

# Total Number of Three-Digit Numbers

A three-digit number can range from 100 to 999. Therefore, the total number of three-digit numbers is 999 - 100 + 1 = 900.

# Number of Three-Digit Multiples of 48

To find the number of three-digit multiples of 48, we need to determine the range of three-digit numbers that are divisible by 48.

The smallest three-digit multiple of 48 is 144 (48 * 3), and the largest three-digit multiple of 48 is 960 (48 * 20). Therefore, the range of three-digit multiples of 48 is from 144 to 960.

To find the number of multiples within this range, we can divide the difference between the largest and smallest multiples by 48 and add 1 to include both ends of the range.

Number of three-digit multiples of 48 = (960 - 144) / 48 + 1 = 816 / 48 + 1 = 17 + 1 = 18.

# Probability Calculation

Now that we know there are 18 three-digit multiples of 48 and a total of 900 three-digit numbers, we can calculate the probability.

Probability = Number of three-digit multiples of 48 / Total number of three-digit numbers = 18 / 900 = 1 / 50.

Therefore, the probability that a randomly chosen three-digit number is divisible by 48 is 1/50.