Question

В ящике находится 70 % стандартных и 30 % нестандартных деталей. Найти вероятность того, что из 5 взятых надачу деталей ровно 4 детали окажутся стандартными

Answer 1

P₅(4)=C₅⁴p⁴·q¹ =[ 5!/(4!·1!) ]·(0,7)⁴·0,3=5·7⁴·3/(10⁵)=0,36015

p=0,7 q=0,3

Answer 2

Calculation of Probability

To find the probability that exactly 4 out of 5 randomly selected parts will be standard, we can use the binomial probability formula. The formula is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where: - P(X = k) is the probability of getting exactly k successes - C(n, k) is the number of combinations of n items taken k at a time - p is the probability of success for each individual trial - n is the total number of trials

In this case, we have: - n = 5 (total number of trials) - k = 4 (number of successes) - p = 0.7 (probability of getting a standard part)

Let's calculate the probability using the formula:

P(X = 4) = C(5, 4) * 0.7^4 * (1-0.7)^(5-4)

Calculating the values:

C(5, 4) = 5 (since there are 5 ways to choose 4 parts out of 5) 0.7^4 = 0.2401 0.3^1 = 0.3

Now, substituting the values into the formula:

P(X = 4) = 5 * 0.2401 * 0.3 = 0.36015

Therefore, the probability that exactly 4 out of 5 randomly selected parts will be standard is approximately 0.36015 or 36.015%.