Question

На должности ассистентов претендуют 4 брюнетки и 5 блондинки. Комиссия выберет 3 из них, независимо от цвета волос. С какой вероятностью среди отобранных кандидатов есть хотя бы одна брюнетка?

Answer 1

Ответ:

0.88 Перша вірогідність це якщо не буде не однієї брюнетки а віднімаємо від 1 то це коли хоча б одна буде

Answer 2

Problem Analysis

We have a total of 9 candidates for the assistant position, consisting of 4 brunettes and 5 blondes. The commission will select 3 candidates, regardless of hair color. We need to find the probability of at least one brunette being among the selected candidates.

Solution

To find the probability of at least one brunette being among the selected candidates, we can use the concept of complementary probability. We will find the probability of none of the selected candidates being brunettes and subtract it from 1.

The probability of none of the selected candidates being brunettes can be calculated by selecting all 3 candidates from the group of blondes only. The number of ways to select 3 candidates from a group of 5 blondes is given by the combination formula:

Number of ways to select 3 blondes = C(5, 3) = 5! / (3! * (5-3)!) = 10

Therefore, the probability of none of the selected candidates being brunettes is 10 out of the total number of ways to select 3 candidates from the total group of 9 candidates.

The total number of ways to select 3 candidates from a group of 9 candidates is given by the combination formula:

Total number of ways to select 3 candidates = C(9, 3) = 9! / (3! * (9-3)!) = 84

Therefore, the probability of at least one brunette being among the selected candidates is:

Probability of at least one brunette = 1 - Probability of none of the selected candidates being brunettes = 1 - 10/84 = 74/84 = 37/42

So, the probability of at least one brunette being among the selected candidates is 37/42.

Answer

The probability of at least one brunette being among the selected candidates is 37/42.