Question

2. В гараже стояли 5 грузовых и 4 легковых машины. Выехали две машины. Какова вероятность того, что обе машины грузовые?

Answer 1

2/7
7-число всех исходов
2-число благоприятных исходов

Answer 2

Problem Analysis

We are given that there are 5 trucks and 4 cars in a garage. Two vehicles are randomly selected and we need to find the probability that both selected vehicles are trucks.

Solution

To find the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total Number of Outcomes: The total number of outcomes is the number of ways we can select any two vehicles from the 9 vehicles in the garage. This can be calculated using the combination formula:

Total Number of Outcomes = C(9, 2) = 9! / (2! * (9-2)!) = 36

Number of Favorable Outcomes: The number of favorable outcomes is the number of ways we can select 2 trucks from the 5 trucks in the garage. This can be calculated using the combination formula:

Number of Favorable Outcomes = C(5, 2) = 5! / (2! * (5-2)!) = 10

Probability: The probability of selecting two trucks is the ratio of the number of favorable outcomes to the total number of outcomes:

Probability = Number of Favorable Outcomes / Total Number of Outcomes = 10 / 36 = 5 / 18

Therefore, the probability that both selected vehicles are trucks is 5/18.