Question

Бросают две игральные кости .Определите вероятность того, что произведение числа выпавших очков делится на 2 ???

Answer 1

Произведение делится на 2 => один из множителей обязан делиться на 2. Т.е. надо найти вероятность того, что хотя бы 1 кубик выпадет четным числом. $P=1-P_{1}*P_{1}$, где $P_{1}$ - вероятность выпадения кубика с нечетным номером (кубики с нечетными номерами выпадают одновременно). $P=1- P_{1}^{2} =1- (3/6)^{2} =3/4$

Answer 2

Probability of the product of the numbers on two dice being divisible by 2

To determine the probability of the product of the numbers on two dice being divisible by 2, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.

The product of the numbers on two dice will be divisible by 2 if at least one of the dice shows an even number. We can calculate this by finding the probability of the complement event, which is the probability that both dice show odd numbers.

The probability of rolling an odd number on a fair six-sided die is 3/6 or 1/2, since there are three odd numbers (1, 3, and 5) out of six possible outcomes. Therefore, the probability of both dice showing odd numbers is (1/2) * (1/2) = 1/4.

The probability of the complement event (at least one even number) is 1 - 1/4 = 3/4.

Therefore, the probability of the product of the numbers on two dice being divisible by 2 is 3/4.