Question

75% продукции производит завод, является продукцией высшего сорта. Какова вероятность того, что с 6 наугад взятых изделий 3 изделия будут изделиями высшего сорта?

Answer 1

3 изделия высшего сорта P=(0.75)^3 
3 изделия не высшего сорта P=(0.25)^3 
число перестановок 6!/(3!*3!)

 

0.75^3 * 0.25^3 * 6! / (3!*3!) = 135/1024 = 0.1318

Answer 2

Calculating the Probability of Selecting High-Quality Products

To calculate the probability of randomly selecting 3 high-quality products out of 6, we can use the concept of combinations and the probability formula.

Given: - 75% of the products are of high quality. - We want to find the probability of selecting 3 high-quality products out of 6.

Using Combinations to Calculate the Probability

We can use the combination formula to calculate the number of ways to choose 3 high-quality products out of 6.

The combination formula is given by: $$ C(n, r) = \frac{n!}{r!(n-r)!} $$

Where: - n = total number of items - r = number of items to be chosen - ! denotes factorial

Calculating the Probability

The probability of selecting 3 high-quality products out of 6 can be calculated using the combination formula and the probability formula.

The probability formula is given by: $$ P(E) = \frac{n(E)}{n(S)} $$

Where: - P(E) = probability of event E - n(E) = number of favorable outcomes - n(S) = total number of outcomes

Applying the Formulas

Let's apply the combination formula to find the number of ways to choose 3 high-quality products out of 6. Then, we can use the probability formula to calculate the probability.

Using the combination formula: $$ C(6, 3) = \frac{6!}{3!(6-3)!} $$

This will give us the number of ways to choose 3 high-quality products out of 6.

Calculating the Probability

Next, we can use the probability formula to calculate the probability of selecting 3 high-quality products out of 6, given that 75% of the products are of high quality.

The probability can be calculated as: $$ P(E) = \frac{n(E)}{n(S)} $$

Where: - n(E) = number of ways to choose 3 high-quality products out of 6 - n(S) = total number of ways to choose 6 products

Let's calculate the probability using the provided information and the formulas.

Final Probability Calculation

The final probability of selecting 3 high-quality products out of 6 can be calculated using the combination formula and the probability formula.