Question

В одной коробке 10 деталей, из них 4 высшего сорта, во второй 15 деталей, из них 6 высшего сорта. Из каждой коробки взяли случайным образом по одной детали. Найти вероятность того, что по крайней мере одна деталь высшего сорта.

Answer 1

Відповідь:

Покрокове пояснення:

Пусть Н1 и Н2 - первая и вторая коробка

А - деталь высшего сорта

Р(А/Н1)=4/10=0.4

Р(А/Н2)=6/15=0.4

Р(А)=Р(А/Н1)×Р(А/Н2)+Р(А/Н1)×(1-Р(А/Н2))+(1-Р(А/Н1))×Р(А/Н2)=0.4²+0.4×0.6+0.6×0.4=0.16+

+2×0.24=0.64

Answer 2

Problem Analysis

We have two boxes, each containing a certain number of parts. From the first box, we randomly select one part, and from the second box, we also randomly select one part. We need to find the probability that at least one of the selected parts is of the highest grade.

Solution

To find the probability, we can use the principle of complementary probability. We will find the probability that none of the selected parts is of the highest grade and subtract it from 1 to get the probability that at least one part is of the highest grade.

Let's calculate the probability step by step.

1. Calculate the probability of selecting a part of the highest grade from the first box: - The first box contains 10 parts, out of which 4 are of the highest grade. - Therefore, the probability of selecting a part of the highest grade from the first box is 4/10.

2. Calculate the probability of selecting a part of the highest grade from the second box: - The second box contains 15 parts, out of which 6 are of the highest grade. - Therefore, the probability of selecting a part of the highest grade from the second box is 6/15.

3. Calculate the probability of not selecting a part of the highest grade from either box: - Since the selections are independent, we can multiply the probabilities from step 1 and step 2 to get the probability of not selecting a part of the highest grade from either box. - The probability of not selecting a part of the highest grade from either box is (4/10) * (6/15).

4. Calculate the probability of at least one part being of the highest grade: - We can subtract the probability from step 3 from 1 to get the probability of at least one part being of the highest grade. - The probability of at least one part being of the highest grade is 1 - (4/10) * (6/15).

Therefore, the probability that at least one part is of the highest grade is 1 - (4/10) * (6/15).

Calculation

Let's calculate the probability:

1 - (4/10) * (6/15) = 1 - (2/5) * (2/5) = 1 - 4/25 = 21/25

Answer

The probability that at least one part is of the highest grade is 21/25.