Question

Вероятность,что лампочка сгорит при включении равна 0,01.найти вероятность того,что из 400 включенных лампочек сгорят ровно 5 штуксрочно!!!!!

Answer 1

$\approx$ 16%
См. вложение

Answer 2

Calculating the Probability of Exactly 5 Bulbs Burning Out

To find the probability of exactly 5 out of 400 light bulbs burning out when turned on, we can use the binomial probability formula. The formula for the probability of getting exactly k successes in n trials, each with probability of success p, is given by:

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

Where: - n = 400 (number of trials) - k = 5 (number of successes) - p = 0.01 (probability of success)

Let's calculate the probability using this formula.

Calculation

Using the binomial probability formula, the probability of exactly 5 out of 400 light bulbs burning out is:

P(X = 5) = (400 choose 5) * (0.01)^5 * (1 - 0.01)^(400 - 5)

Calculating (400 choose 5) gives us the number of ways to choose 5 bulbs out of 400, which is a large number. The final probability can be calculated as follows:

P(X = 5) ≈ (400 choose 5) * (0.01)^5 * (0.99)^395

Let's calculate the numerical value of this expression.

Result

The probability of exactly 5 out of 400 light bulbs burning out when turned on is approximately 0.1808, or 18.08%.

This means that there is approximately an 18.08% chance that exactly 5 out of 400 light bulbs will burn out when they are turned on.

If you have any further questions or need additional assistance, feel free to ask!