Question

По одному разу пiдкидають три гральнi кубики. Яка ймовiрнiсть того, що а) хоча б на двох кубиках випаде однакова кiлькiсть очок? б) на всiх трьох випаде однакова кiлькiсть очок?

Answer 1

Ответ:

А) 6*1*6=36

б) 6*5*6=180

Пошаговое объяснение:

Answer 2

Probability of getting the same number of points on at least two dice:

To calculate the probability of getting the same number of points on at least two dice, we can consider the complementary event, which is the probability of not getting the same number of points on any two dice.

Let's break down the problem into two cases:

Case a) At least two dice have the same number of points:

To calculate this probability, we can consider the opposite event, which is the probability of all three dice having different numbers of points.

The first die can have any number from 1 to 6. The second die can have any number except the number obtained on the first die, which leaves us with 5 possibilities. Similarly, the third die can have any number except the numbers obtained on the first two dice, which leaves us with 4 possibilities.

Therefore, the probability of all three dice having different numbers of points is (5/6) * (4/6) = 20/36 = 5/9.

The probability of at least two dice having the same number of points is the complement of the above probability, which is 1 - 5/9 = 4/9.

Case b) All three dice have the same number of points:

To calculate this probability, we need to consider the probability of getting the same number of points on all three dice.

The first die can have any number from 1 to 6. The second die must also have the same number of points as the first die, which has a probability of 1/6. Similarly, the third die must also have the same number of points as the first two dice, which also has a probability of 1/6.

Therefore, the probability of all three dice having the same number of points is (1/6) * (1/6) = 1/36.

Summary:

a) The probability of at least two dice having the same number of points is 4/9.

b) The probability of all three dice having the same number of points is 1/36.

Please note that these probabilities assume fair dice and that each die is independent of the others.