Question

Вероятность забросить мяч у баскетболиста равна 0,6. проведено 8 бросков. какова вероятность 5 попаданий? с решением , если можно

Answer 1

Применяем формулу Бернулли:
$P=C_n^m*p^m*q^{n-m}\\\\n=8\\m=5\\p=0,6\\q=1-p=1-0,6=0,4\\\\P=C_8^5*(0,6)^5*(0,4)^3= \frac{8!}{5!3!}*0,07776*0,064\approx0,2787$
(или 27,87%)

Answer 2

Probability of Making 5 Shots in 8 Attempts

To calculate the probability of making 5 shots in 8 attempts, we can use the binomial probability formula. The formula for the probability of getting exactly k successes in n trials, when the probability of success on a single trial is p, is given by:

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

Where: - n = 8 (number of trials/attempts) - k = 5 (number of successes) - p = 0.6 (probability of success on a single trial)

Plugging these values into the formula, we get:

P(X = 5) = (8 choose 5) * (0.6)^5 * (1 - 0.6)^(8 - 5)

Calculating the values: - (8 choose 5) = 56 - (0.6)^5 ≈ 0.07776 - (1 - 0.6)^(8 - 5) = (0.4)^3 = 0.064

Now, we can calculate the probability: P(X = 5) ≈ 56 * 0.07776 * 0.064 ≈ 0.280

So, the probability of making 5 shots in 8 attempts is approximately 0.280.

Conclusion

The probability of making 5 shots in 8 attempts, given a 0.6 probability of making a shot, is approximately 0.280.