Question

Лена четырежды брасает игральный кубик.в сумме у неё выпадает 7 очков.найдите вероятность того,что при втором броске у неё выпало 4 очка

Answer 1

Всего существует 36 комбинаций игральных кубиков.

Для числа 4 существует 3 комбинации: 2-2, 3-1, 1-3

Следовательно вероятность выпадения четверки равна 3/36=1/12=8,3%

Answer 2

Problem Analysis

Lena is rolling a six-sided die four times, and the sum of the numbers that she rolls is 7. We need to find the probability that she rolls a 4 on the second roll.

Solution

To find the probability of rolling a 4 on the second roll, we need to consider the total number of possible outcomes and the number of favorable outcomes.

# Total Number of Outcomes

When rolling a six-sided die, there are 6 possible outcomes on each roll. Since Lena rolls the die four times, the total number of possible outcomes is 6^4 = 1296.

# Number of Favorable Outcomes

To determine the number of favorable outcomes, we need to consider the condition that the sum of the numbers rolled is 7. We can use a systematic approach to count the number of ways this can happen.

Let's consider the possible outcomes for the first roll: - If Lena rolls a 1 on the first roll, she needs to roll a 6 on the second roll to get a sum of 7. - If Lena rolls a 2 on the first roll, she needs to roll a 5 on the second roll to get a sum of 7. - If Lena rolls a 3 on the first roll, she needs to roll a 4 on the second roll to get a sum of 7. - If Lena rolls a 4 on the first roll, she needs to roll a 3 on the second roll to get a sum of 7. - If Lena rolls a 5 on the first roll, she needs to roll a 2 on the second roll to get a sum of 7. - If Lena rolls a 6 on the first roll, she needs to roll a 1 on the second roll to get a sum of 7.

Therefore, there are 6 possible outcomes for the first roll that lead to a sum of 7. For each of these outcomes, Lena has 6 possible outcomes for the second roll. So, the number of favorable outcomes is 6 * 6 = 36.

# Probability Calculation

To calculate the probability, we divide the number of favorable outcomes by the total number of outcomes:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

Plugging in the values, we get:

Probability = 36 / 1296 = 1 / 36

Therefore, the probability that Lena rolls a 4 on the second roll is 1/36.