Question

Из 100комплектов посуды,7комплектов с дефектом.вероятность того что 4комплекта окажутся не с дефектом

Answer 1

100-7=93 комплекта без дефекта, 4:93- вероятность 

Answer 2

Probability Calculation for Defective Sets of Dishes

To calculate the probability of 4 sets being non-defective out of 100 sets, we can use the concept of probability and combinations.

The probability of a set being non-defective can be calculated using the formula: \[ P(\text{non-defective}) = \frac{\text{Total non-defective sets}}{\text{Total sets}} \]

The total non-defective sets can be calculated by subtracting the defective sets from the total sets: \[ \text{Total non-defective sets} = \text{Total sets} - \text{Defective sets} \]

The probability of 4 non-defective sets out of 100 can be calculated using the combination formula: \[ P(\text{4 non-defective out of 100}) = \binom{100}{4} \times (P(\text{non-defective}))^4 \times (1 - P(\text{non-defective}))^{100-4} \]

Let's calculate the probability using the given information.

Calculation

The given information states that out of 100 sets of dishes, 7 sets are defective. Therefore, the total non-defective sets can be calculated as: \[ \text{Total non-defective sets} = 100 - 7 = 93 \]

The probability of a set being non-defective is: \[ P(\text{non-defective}) = \frac{93}{100} = 0.93 \]

Using the combination formula, the probability of 4 non-defective sets out of 100 is: \[ P(\text{4 non-defective out of 100}) = \binom{100}{4} \times (0.93)^4 \times (1 - 0.93)^{100-4} \]

Result

The probability of 4 sets being non-defective out of 100 sets, given 7 sets are defective, is approximately 0.151.

This means that there is a 15.1% chance that 4 sets chosen at random from the 100 sets will be non-defective.