Question

Найти вероятность того, что событие А появится в пяти независимых испытаниях не менее двух раз, если в каждом испытании вероятность появления события А равна 0.3

Answer 1

я так думаю

пять раз по 0,3 - это 1,5

два раз по 0,3 - это 0,6

Таким образом, первое есть n(общее количество вариантов), а второе - m (количество полезных вариантов)

Тогда вероятность будет m/n=0.4

Answer 2

Calculating the Probability

To find the probability that event A appears at least twice in five independent trials, we can use the binomial probability formula. The formula is as follows:

P(X ≥ k) = 1 - P(X < k)

Where: - P(X ≥ k) is the probability that the event occurs at least k times, - P(X < k) is the probability that the event occurs less than k times.

In this case, event A has a probability of 0.3 of occurring in each trial. Therefore, the probability of event A not occurring in each trial (q) is 1 - 0.3 = 0.7.

Using the formula, we can calculate the probability as follows:

P(X ≥ 2) = 1 - P(X < 2)

Let's calculate the probability step by step:

1. Calculate the probability of event A occurring exactly 0 times in 5 trials: - P(X = 0) = (0.7)^5 = 0.16807

2. Calculate the probability of event A occurring exactly 1 time in 5 trials: - P(X = 1) = 5C1 * (0.3)^1 * (0.7)^4 = 0.36015

3. Calculate the probability of event A occurring less than 2 times: - P(X < 2) = P(X = 0) + P(X = 1) = 0.16807 + 0.36015 = 0.52822

4. Calculate the probability of event A occurring at least 2 times: - P(X ≥ 2) = 1 - P(X < 2) = 1 - 0.52822 = 0.47178

Therefore, the probability that event A appears at least twice in five independent trials, given that the probability of event A in each trial is 0.3, is approximately 0.47178.