Question

Василий очень не любит бегать. Но он решил по утрам делать пробежку для здоровья. Вероятность того, что Василий на пробежке преодолеет больше 300 метров, равна 0,86, а вероятность того, что он пробежит более 700 метров, равна 0,68. Какова вероятность, что Василий пробежит более 300 метров, но не более 700 метров?

Answer 1

Ответ:

Пусть A - "Василий на пробежке преодолеет больше 300 метров, но меньше 700 метров", Б - "Василий пробежит более 700 метров", В - "Василий пробежит ровно 700 метров", тогда A + Б + В - "Василий пробежит больше 300 метров".

P(A + Б + В) = P(A) + P(Б) + P(В)= P(A) + P(Б);

0,86 = P(А) + 0,68

P(А) = 0,86 - 0,68 = 0,18

Ответ: Вероятность того, что Василий пробежит более 300 метров, но меньше 700 метров, равна 0,18

Answer 2

Probability of Vasily running more than 300 meters

The probability of Vasily running more than 300 meters is given as 0.86.

Probability of Vasily running more than 700 meters

The probability of Vasily running more than 700 meters is given as 0.68.

Probability of Vasily running more than 300 meters but not more than 700 meters

To find the probability of Vasily running more than 300 meters but not more than 700 meters, we need to subtract the probability of him running more than 700 meters from the probability of him running more than 300 meters.

Let's denote: - A: Vasily running more than 300 meters - B: Vasily running more than 700 meters

We know that P(A) = 0.86 and P(B) = 0.68.

To find the probability of Vasily running more than 300 meters but not more than 700 meters, we can use the formula: P(A and not B) = P(A) - P(A and B)

Since we don't have the probability of Vasily running more than 300 meters and more than 700 meters, we cannot calculate the exact probability of Vasily running more than 300 meters but not more than 700 meters.

However, we can make an assumption that the events A and B are independent. In that case, we can use the formula: P(A and not B) = P(A) - P(A) * P(B)

Substituting the values, we get: P(A and not B) = 0.86 - 0.86 * 0.68

Calculating this, we find that the probability of Vasily running more than 300 meters but not more than 700 meters is approximately 0.7236.

Please note that this calculation assumes independence between the events A and B, which may or may not be accurate in this context.