A class has 6 girls and 4 boys. A committee of 3 is to be randomly selected. What is the probability of each event?All 3 people selected are girls.Only 1 person selected is a girl.At least 2 people selected are boys.
Question
A class has 6 girls and 4 boys. A committee of 3 is to be randomly selected. What is the probability of each event?All 3 people selected are girls.Only 1 person selected is a girl.At least 2 people selected are boys.
Solution
To solve this problem, we will use the concept of combinations in probability.
- All 3 people selected are girls:
The total number of ways to select 3 students out of 10 is C(10,3) = 120.
The number of ways to select 3 girls out of 6 is C(6,3) = 20.
So, the probability that all 3 selected are girls is 20/120 = 1/6.
- Only 1 person selected is a girl:
The number of ways to select 1 girl out of 6 is C(6,1) = 6.
The number of ways to select 2 boys out of 4 is C(4,2) = 6.
So, the number of ways to select 1 girl and 2 boys is 6*6 = 36.
So, the probability that only 1 selected is a girl is 36/120 = 3/10.
- At least 2 people selected are boys:
This can happen in two ways - either 2 boys and 1 girl, or 3 boys.
The number of ways to select 2 boys out of 4 is C(4,2) = 6.
The number of ways to select 1 girl out of 6 is C(6,1) = 6.
So, the number of ways to select 2 boys and 1 girl is 6*6 = 36.
The number of ways to select 3 boys out of 4 is C(4,3) = 4.
So, the total number of ways to select at least 2 boys is 36 + 4 = 40.
So, the probability that at least 2 selected are boys is 40/120 = 1/3.
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