Question

Игральный кубик подбрасывают 2 раза.Найдите вероятность того,что шестерка выпадает ровно один раз.

Answer 1

Вероятность выпадения шестерки 1/6, она выпадет или в первый раз ли во второй
P=1/6*5/6+5/6*1/6=10/36=5/18

Answer 2

Calculating the Probability of Rolling a Six Exactly Once

To find the probability of rolling a six exactly once when a fair die is rolled twice, we need to consider the possible outcomes.

There are two ways in which a six can be rolled exactly once: 1. The first roll is a six, and the second roll is not a six. 2. The first roll is not a six, and the second roll is a six.

Let's calculate the probability for each case:

1. The probability of rolling a six on the first roll is 1/6. - Source 2. The probability of not rolling a six on the first roll is 5/6. - Source 3. The probability of rolling a six on the second roll, given that the first roll was not a six, is also 1/6. - Source Now, we can calculate the overall probability by multiplying the probabilities of each case:

Case 1: (Probability of rolling a six on the first roll) * (Probability of not rolling a six on the second roll) = (1/6) * (5/6) = 5/36

Case 2: (Probability of not rolling a six on the first roll) * (Probability of rolling a six on the second roll) = (5/6) * (1/6) = 5/36

Finally, we add the probabilities of both cases to get the overall probability:

Overall probability = Case 1 + Case 2 = 5/36 + 5/36 = 10/36 = 5/18

Therefore, the probability of rolling a six exactly once when a fair die is rolled twice is 5/18.

Please let me know if you need any further clarification or assistance!