Question

в корзине 10 яблок,из которых четыре зеленых. На удачу достали три яблока. Найти вероятность того,что хотя бы одно из выбранных яблок зеленое.

Answer 1

Число зеленых яблок делим на число всех яблок

Answer 2

Problem Analysis

We have a basket with 10 apples, 4 of which are green. We randomly select 3 apples from the basket. We need to find the probability that at least one of the selected apples is green.

Solution

To find the probability, we need to calculate the number of favorable outcomes (at least one green apple) and the total number of possible outcomes.

The total number of possible outcomes is the number of ways we can select 3 apples from a basket of 10 apples, which can be calculated using the combination formula:

Total number of possible outcomes = C(10, 3)

The number of favorable outcomes is the number of ways we can select at least one green apple from the basket. We can calculate this by considering two cases: 1. Selecting exactly one green apple and two non-green apples. 2. Selecting two green apples and one non-green apple.

For the first case, we can calculate the number of ways to select one green apple from 4 green apples and two non-green apples from 6 non-green apples:

Number of ways to select one green apple and two non-green apples = C(4, 1) * C(6, 2)

For the second case, we can calculate the number of ways to select two green apples from 4 green apples and one non-green apple from 6 non-green apples:

Number of ways to select two green apples and one non-green apple = C(4, 2) * C(6, 1)

The total number of favorable outcomes is the sum of the favorable outcomes from both cases:

Total number of favorable outcomes = Number of ways to select one green apple and two non-green apples + Number of ways to select two green apples and one non-green apple

Finally, we can calculate the probability by dividing the total number of favorable outcomes by the total number of possible outcomes:

Probability = Total number of favorable outcomes / Total number of possible outcomes

Let's calculate the probability.

Calculation

Using the formulas mentioned above, we can calculate the probability as follows:

Total number of possible outcomes = C(10, 3) = 120

Number of ways to select one green apple and two non-green apples = C(4, 1) * C(6, 2) = 4 * 15 = 60

Number of ways to select two green apples and one non-green apple = C(4, 2) * C(6, 1) = 6 * 6 = 36

Total number of favorable outcomes = 60 + 36 = 96

Probability = Total number of favorable outcomes / Total number of possible outcomes = 96 / 120 = 0.8

Answer

The probability that at least one of the selected apples is green is 0.8.