Question

Найти вероятность того,что событие А появится не менее трех раз в четырех независимых испытаниях,если вероятность появления события А в одном испытании равно 0,4.

Answer 1

я ваще не в 10 и не в 11

 

Answer 2

Calculating the Probability of Event A Appearing at Least Three Times

To find the probability of event A appearing not less than three times in four independent trials, given the probability of event A in one trial is 0.4, we can use the binomial probability formula.

The probability of event A appearing exactly k times in n trials is given by the formula: P(X=k) = (n choose k) * (p^k) * ((1-p)^(n-k))

Where: - n = number of trials - k = number of successful events - p = probability of success in one trial - (n choose k) = n! / (k! * (n-k)!)

Using this formula, we can calculate the probability of event A appearing at least three times in four trials with p=0.4.

Calculation

Using the binomial probability formula, we can calculate the probability of event A appearing at least three times in four trials with p=0.4.

The probability of event A appearing at least three times in four trials is given by: P(X>=3) = P(X=3) + P(X=4)

Where: - P(X=3) = (4 choose 3) * (0.4^3) * (0.6^1) - P(X=4) = (4 choose 4) * (0.4^4) * (0.6^0)

Let's calculate these probabilities.

Calculation

- P(X=3) = (4 choose 3) * (0.4^3) * (0.6^1) = (4! / (3! * (4-3)!) ) * (0.4^3) * (0.6^1) = 4 * 0.064 * 0.6 = 0.1536 - P(X=4) = (4 choose 4) * (0.4^4) * (0.6^0) = (4! / (4! * (4-4)!) ) * (0.4^4) * (0.6^0) = 1 * 0.0256 * 1 = 0.0256

Therefore, the probability of event A appearing at least three times in four trials is: P(X>=3) = P(X=3) + P(X=4) = 0.1536 + 0.0256 = 0.1792

So, the probability of event A appearing not less than three times in four independent trials, with the probability of event A in one trial being 0.4, is 0.1792.

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