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In a class of 12 boys and 8 girls, a committee of three should be formed. What is the probability that there are at least two girls on the committee?

User Kampau Ocu
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1 Answer

3 votes

Answer:

34.94%

Explanation:

To find the probability that there are at least two girls on the committee, we need to calculate the probability of two girls on the committee and the probability of three girls on the committee, and then add them together.

Total number of ways to form a committee of 3 from 20 students (12 boys + 8 girls) = Combination(20, 3) = 1140

Probability of two girls on the committee:

Number of ways to choose 2 girls from 8 girls = Combination(8, 2) = 28

Number of ways to choose 1 boy from 12 boys = Combination(12, 1) = 12

Total number of ways to have 2 girls and 1 boy on the committee = 28 * 12 = 336

Probability of two girls on the committee = 336 / 1140 = 14 / 47

Probability of three girls on the committee:

Number of ways to choose 3 girls from 8 girls = Combination(8, 3) = 56

Probability of three girls on the committee = 56 / 1140 = 7 / 190

Now, we add the probabilities of two girls and three girls on the committee:

Total probability of having at least two girls on the committee = Probability of two girls + Probability of three girls

Total probability = (14/47) + (7/190)

Total probability = 665 / 1903

So, the probability that there are at least two girls on the committee is 665/1903, which is approximately 0.3494 or about 34.94%.

User Osa E
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