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From a group of 5 boys and 3 girls, 3 persons are chosen at random. Then the probability that there are more girls than boys is:
- a)15/28
- b)15/56
- c)1
- d)2/7
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
From a group of 5 boys and 3 girls, 3 persons are chosen at random. Th...
There are 3 girls and 5 boys
∴ Total number of boys and girls = 8
n(s) = Total number of ways of choosing 3 persons
Let E be the event that there are more girls than boys.
⇒ (2 girls & 1 boy) or (3 girls & 0 boy)
∴ Total number of boys and girls = 8
n(s) = Total number of ways of choosing 3 persons
Let E be the event that there are more girls than boys.
⇒ (2 girls & 1 boy) or (3 girls & 0 boy)
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From a group of 5 boys and 3 girls, 3 persons are chosen at random. Th...
Given:
- 5 boys and 3 girls
- 3 persons are chosen at random
To find:
- Probability that there are more girls than boys
Solution:
Total number of ways of choosing 3 persons out of 8 is:
8C3 = (8 × 7 × 6) / (3 × 2 × 1) = 56
Number of ways of choosing 3 persons such that there are more girls than boys:
- 3 girls and 0 boys can be chosen in 3C3 × 5C0 = 1 × 1 = 1 way
- 2 girls and 1 boy can be chosen in 3C2 × 5C1 = 3 × 5 = 15 ways
- 1 girl and 2 boys can be chosen in 3C1 × 5C2 = 3 × 10 = 30 ways
Total number of ways of choosing 3 persons such that there are more girls than boys is:
1 + 15 + 30 = 46
Probability of choosing 3 persons such that there are more girls than boys is:
46/56 = 2/7
Therefore, the correct answer is option D (2/7).
- 5 boys and 3 girls
- 3 persons are chosen at random
To find:
- Probability that there are more girls than boys
Solution:
Total number of ways of choosing 3 persons out of 8 is:
8C3 = (8 × 7 × 6) / (3 × 2 × 1) = 56
Number of ways of choosing 3 persons such that there are more girls than boys:
- 3 girls and 0 boys can be chosen in 3C3 × 5C0 = 1 × 1 = 1 way
- 2 girls and 1 boy can be chosen in 3C2 × 5C1 = 3 × 5 = 15 ways
- 1 girl and 2 boys can be chosen in 3C1 × 5C2 = 3 × 10 = 30 ways
Total number of ways of choosing 3 persons such that there are more girls than boys is:
1 + 15 + 30 = 46
Probability of choosing 3 persons such that there are more girls than boys is:
46/56 = 2/7
Therefore, the correct answer is option D (2/7).
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