Question

Игральную кость бросают 720 раз. Какова вероятность того, что при этом три очка выпало: 120 раз?

Answer 1

Ответ:

120

Пошаговое объяснение:

720:6=120

Answer 2

Probability of Getting Three Sixes in 720 Rolls of a Die

To calculate the probability of getting three sixes in 720 rolls of a die, we can use the formula for the probability of an event:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

In this case, the favorable outcome is getting three sixes, and the total number of outcomes is 720 rolls.

Calculation

The probability of getting a six on a single roll of a fair six-sided die is 1/6. Since each roll is independent, the probability of getting three sixes in a row is calculated as follows:

Probability = (1/6) * (1/6) * (1/6)

Probability = (1/216)

So, the probability of getting three sixes in a single roll is 1/216.

Applying to 720 Rolls

To find the probability of getting three sixes in 720 rolls, we can use the binomial probability formula:

P(x) = (n choose x) * (p^x) * (q^(n-x))

Where: - n = total number of trials (in this case, 720 rolls) - x = number of successful trials (in this case, 120 sixes) - p = probability of success on an individual trial (in this case, 1/6 for getting a six) - q = probability of failure on an individual trial (in this case, 5/6)

Using this formula, we can calculate the probability of getting exactly 120 sixes in 720 rolls.

Calculation

P(120) = (720 choose 120) * ((1/6)^120) * ((5/6)^(720-120))

This calculation gives us the probability of getting exactly 120 sixes in 720 rolls.

Conclusion

The probability of getting exactly 120 sixes in 720 rolls of a fair six-sided die is the result of the above calculation.