Question

Вася стоит на автобусной остановке. Там останавливаются автобусы маршрутов А и Б, причём Васе подходит только один из их. Вероятность того, что придёт подходящий автобус, равна 0,7. Найдите вероятность того, ЧТО НИ ОДИН ИЗ ТРЕХ БЛИЖАЙШИХ АВТОБУСОВ НЕ ПОДХОДИТ ВАСЕ.

Answer 1

Вероятность того, что придёт неподходящий автобус P(B)=1-0,7=0,3

Вероятность того, что ни один из трёх ближайших автобусов не подходит Васе P=0,3*0,3*0,3=0,027

Answer 2

Probability of the Suitable Bus Arriving

Vasya is waiting at a bus stop where buses of routes A and B stop, and only one of them is suitable for Vasya. The probability of the suitable bus arriving is 0.7.

Probability that None of the Three Nearest Buses is Suitable for Vasya

To find the probability that none of the three nearest buses is suitable for Vasya, we can use the concept of complementary events. The probability of the complementary event (at least one of the three nearest buses is suitable) is easier to calculate, and then we can subtract it from 1 to find the probability of the event of interest.

The probability of at least one of the three nearest buses being suitable for Vasya can be calculated using the concept of the complement: 1 - (probability that the first bus is not suitable) * (probability that the second bus is not suitable) * (probability that the third bus is not suitable)

Let's calculate the probability of at least one of the three nearest buses being suitable for Vasya: 1 - (0.3 * 0.3 * 0.3) = 0.973

Now, to find the probability that none of the three nearest buses is suitable for Vasya, we subtract the above result from 1: 1 - 0.973 = 0.027

Therefore, the probability that none of the three nearest buses is suitable for Vasya is 0.027.