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The ratio of the number of girls to the number of boys is the 5 : 2 in a class of 21 students. A group of three students is to to be selected at random amongst them. What is the probability that the selected group of students contain one boy and two girls?
  • a)
    45/266
  • b)
    32/343
  • c)
    120/217
  • d)
    46/267
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The ratio of the number of girls to the number of boys is the 5 : 2 in...
5:2 = 15+6 = 21
n(S) = 21C3 = 1330
n(E) = 15C1 x 6C2 = 15 x 15 = 225
P = 225/1330 = 45/266
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Most Upvoted Answer
The ratio of the number of girls to the number of boys is the 5 : 2 in...
Given:
- Ratio of girls to boys = 5 : 2
- Total students = 21

We can find the number of girls and boys in the class as follows:

- Let the number of girls be 5x and the number of boys be 2x
- Total number of students = 21
- Therefore, 5x + 2x = 21
- Solving for x, we get x = 3
- So, there are 15 girls and 6 boys in the class

Now, we need to find the probability of selecting a group of 3 students with one boy and two girls.

We can use the formula for probability:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

Number of favorable outcomes:
- We need to select 1 boy from 6 boys and 2 girls from 15 girls
- Number of ways to select 1 boy from 6 boys = 6C1 = 6
- Number of ways to select 2 girls from 15 girls = 15C2 = 105
- Total number of favorable outcomes = 6 * 105 = 630

Total number of outcomes:
- We need to select 3 students from a total of 21 students
- Total number of ways to select 3 students from 21 students = 21C3 = 1330

Putting the values in the formula for probability, we get:

Probability = 630/1330 = 45/95 = 9/19

Therefore, the correct answer is option A) 45/266.
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The ratio of the number of girls to the number of boys is the 5 : 2 in a class of 21 students. A group of three students is to to be selected at random amongst them. What is the probability that the selected group of students contain one boy and two girls?a)45/266b)32/343c)120/217d)46/267e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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