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Four members are to be chosen from a group of 3 women and 4 children. Find the probability of selecting exactly 3 children.
- a)3/50
- b)12/25
- c)1/5
- d)12/35
- e)1/7
Correct answer is option 'D'. Can you explain this answer?
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Four members are to be chosen from a group of 3 women and 4 children. ...
To find the probability of selecting exactly 3 children from a group of 3 women and 4 children, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
The total number of possible outcomes is the number of ways to choose 4 members from a group of 7. This can be calculated using the combination formula:
nCr = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be chosen.
In this case, we have 7 members to choose from and we want to choose 4, so the total number of possible outcomes is:
7C4 = 7! / (4!(7-4)!) = 7! / (4!3!) = (7 x 6 x 5)/(3 x 2 x 1) = 35
Number of favorable outcomes:
To select exactly 3 children, we need to choose 3 children from the 4 available and 1 member from the 3 women. This can be calculated using the combination formula:
nCr = n! / (r!(n-r)!)
In this case, we want to choose 3 children from 4 and 1 woman from 3, so the number of favorable outcomes is:
4C3 x 3C1 = (4! / (3!(4-3)!) ) x (3! / (1!(3-1)!)) = (4 x 3) x (3) = 12
Probability:
The probability of selecting exactly 3 children is given by the number of favorable outcomes divided by the total number of possible outcomes:
P(exactly 3 children) = favorable outcomes / total outcomes
P(exactly 3 children) = 12 / 35
Therefore, the correct answer is option D) 12/35.
Total number of possible outcomes:
The total number of possible outcomes is the number of ways to choose 4 members from a group of 7. This can be calculated using the combination formula:
nCr = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be chosen.
In this case, we have 7 members to choose from and we want to choose 4, so the total number of possible outcomes is:
7C4 = 7! / (4!(7-4)!) = 7! / (4!3!) = (7 x 6 x 5)/(3 x 2 x 1) = 35
Number of favorable outcomes:
To select exactly 3 children, we need to choose 3 children from the 4 available and 1 member from the 3 women. This can be calculated using the combination formula:
nCr = n! / (r!(n-r)!)
In this case, we want to choose 3 children from 4 and 1 woman from 3, so the number of favorable outcomes is:
4C3 x 3C1 = (4! / (3!(4-3)!) ) x (3! / (1!(3-1)!)) = (4 x 3) x (3) = 12
Probability:
The probability of selecting exactly 3 children is given by the number of favorable outcomes divided by the total number of possible outcomes:
P(exactly 3 children) = favorable outcomes / total outcomes
P(exactly 3 children) = 12 / 35
Therefore, the correct answer is option D) 12/35.
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Four members are to be chosen from a group of 3 women and 4 children. Find the probability of selecting exactly 3 children.a)3/50b)12/25c)1/5d)12/35e)1/7Correct answer is option 'D'. Can you explain this answer?
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