Question

Наугад взято двухзначное число.Какова вероятность того,что это число является квадратом натурального числа? Кубом натурального числа? Четвёртой степенью натурального числа?Помогите пожалуйста!=)

Answer 1

Начнем с того что всего двузначных чисел (число всех исходов) равно 99-9=90 всего квадратов натуральных чисел  4^2   до  9^2=81  6     кубов     3^3 до 4^3=64 2)  четвертых степеней   2^4  до  3^4=81   2  тогда искомые вероятности  6/90  2/90 2/90  или   1/15  1/45 1/45

Answer 2

Probability of a Two-Digit Number Being a Perfect Square, Cube, or Fourth Power

To calculate the probability of a randomly chosen two-digit number being a perfect square, cube, or fourth power, we can consider the following:

Perfect Square: - A perfect square is a number that can be expressed as the product of an integer with itself. - In the range of two-digit numbers (10 to 99), the perfect squares are 16, 25, 36, 49, 64, 81. - Therefore, there are 6 perfect squares in the range of two-digit numbers.

Perfect Cube: - A perfect cube is a number that can be expressed as the product of an integer with itself twice. - In the range of two-digit numbers (10 to 99), the perfect cubes are 27 and 64. - Therefore, there are 2 perfect cubes in the range of two-digit numbers.

Fourth Power: - A number raised to the fourth power is a number that has been multiplied by itself four times. - In the range of two-digit numbers (10 to 99), the fourth powers are 16 and 81. - Therefore, there are 2 fourth powers in the range of two-digit numbers.

Calculating the Probability

To calculate the probability of a randomly chosen two-digit number being a perfect square, cube, or fourth power, we can use the following formula:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Total number of possible outcomes = 90 (from 10 to 99, inclusive)

Number of favorable outcomes: - For perfect squares: 6 - For perfect cubes: 2 - For fourth powers: 2

Probability of being a perfect square = 6 / 90 = 1 / 15 Probability of being a perfect cube = 2 / 90 = 1 / 45 Probability of being a fourth power = 2 / 90 = 1 / 45

Therefore, the probability of a randomly chosen two-digit number being a perfect square is 1/15, being a perfect cube is 1/45, and being a fourth power is 1/45.