Question

В коробке находятся шары с номерами 1.2.3.4.5. из коробки вынимают два шара. какова вероятность того, что сумма номеров на них равна 5

Answer 1

Вероятность 2к5 либо 1и4    либо 3и2 

Answer 2

Calculating the Probability of Drawing Two Balls with a Sum of 5

To calculate the probability of drawing two balls from the box with numbers 1, 2, 3, 4, and 5, such that the sum of the numbers on the balls is equal to 5, we can use the concept of combinations and probability.

The possible combinations of two balls that sum to 5 are: - 1 and 4 - 2 and 3 - 3 and 2 - 4 and 1

The total number of ways to choose 2 balls out of 5 is given by the combination formula: $$ C(n, k) = \frac{n!}{k!(n-k)!} $$

Where: - n = total number of items - k = number of items to choose

The probability of each combination can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Calculation

1. Total Possible Combinations: Using the combination formula, we can calculate the total possible combinations of choosing 2 balls out of 5: $$ C(5, 2) = \frac{5!}{2!(5-2)!} = \frac{5*4}{2} = 10 $$ 2. Favorable Combinations: There are 4 favorable combinations that sum to 5: (1, 4), (2, 3), (3, 2), and (4, 1).

3. Probability: The probability of drawing two balls with a sum of 5 is the ratio of favorable combinations to total possible combinations: $$ P = \frac{\text{Number of Favorable Combinations}}{\text{Total Possible Combinations}} = \frac{4}{10} = 0.4 $$

Answer

The probability of drawing two balls from the box with numbers 1, 2, 3, 4, and 5, such that the sum of the numbers on the balls is equal to 5, is 0.4.