Question

Вероятность того что при бросании игральной кости выпало число очков кратное 3

Answer 1

На игральной кости шесть вариантов чисел: 1,2.3,4,5,6. Из них кратно 3 два варианта: 3 и 6. Таким образом, из шести возможных результатов два нам подходят. Соответственно, вероятность выпадения одного из них 2/6 = 1/3.

Answer 2

Probability of Rolling a Multiple of 3 on a Six-Sided Die

When rolling a six-sided die, the probability of rolling a number that is a multiple of 3 can be calculated using the concept of probability and the total number of favorable outcomes.

The probability of rolling a number that is a multiple of 3 on a six-sided die is 1/2 or 0.5.

The calculation for the probability of rolling a multiple of 3 on a six-sided die is as follows: - Total number of outcomes, n = 6 - Number of favorable outcomes, k = 3 - Probability, p = 1/2

Using the formula for probability, which is $P=P_n(k)=C_n^k \cdot p^k \cdot (1-p)^{n-k}$, the probability of rolling a multiple of 3 (k=3) on a six-sided die (n=6) is: $$ P_6(3)=C_6^3 \cdot \left(1/2\right)^3 \cdot \left(1-1/2\right)^3=20 \cdot \left(1/2\right)^3=1/2=0.5 $$

Therefore, the probability of rolling a number that is a multiple of 3 on a six-sided die is 0.5 or 50%.

This means that when rolling a six-sided die, there is a 50% chance of rolling a number that is a multiple of 3.

Conclusion

The probability of rolling a number that is a multiple of 3 on a six-sided die is 0.5 or 50%.