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Out of 128 families with 4 children each, how many are expected to have at least one boy and one girl?
- a)100.
- b)105.
- c)108.
- d)112.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Out of 128 families with 4 children each, how many are expected to hav...
Step-by-step explanation:
4children in a family can be in
2 x 2 x 2 x2 = 16 ways
at least one boy and one girl =
Total cases - all boys - all girs
All boys = 1 case
All girls = 1 case
=> at least one boy and one girl = 16 - 1 - 1 = 14
Probability of at least one boy and one girl = 14/16
out of 128 families expected to have = 128 x 14/16 = 8 x 14
= 112
112 Families expected to have at least one boy and one girl.
4children in a family can be in
2 x 2 x 2 x2 = 16 ways
at least one boy and one girl =
Total cases - all boys - all girs
All boys = 1 case
All girls = 1 case
=> at least one boy and one girl = 16 - 1 - 1 = 14
Probability of at least one boy and one girl = 14/16
out of 128 families expected to have = 128 x 14/16 = 8 x 14
= 112
112 Families expected to have at least one boy and one girl.
Most Upvoted Answer
Out of 128 families with 4 children each, how many are expected to hav...
Given: 128 families with 4 children each
To find: How many are expected to have at least one boy and one girl?
Solution:
We can solve this problem using the principle of inclusion and exclusion.
Total number of ways of having 4 children in a family = 2^4 = 16 (as each child can be either a boy or a girl)
Number of ways of having only boys in a family = 1 (BBBB)
Number of ways of having only girls in a family = 1 (GGGG)
Number of ways of having no boys in a family = 1 (GGGG)
Number of ways of having no girls in a family = 1 (BBBB)
Number of ways of having at least one boy and one girl in a family = Total number of ways - Number of ways of having only boys - Number of ways of having only girls - Number of ways of having no boys - Number of ways of having no girls
= 16 - 1 - 1 - 1 - 1
= 12
Expected number of families with at least one boy and one girl = Total number of families x probability of having at least one boy and one girl
= 128 x (12/16)
= 96
Therefore, the correct option is (D) 112.
To find: How many are expected to have at least one boy and one girl?
Solution:
We can solve this problem using the principle of inclusion and exclusion.
Total number of ways of having 4 children in a family = 2^4 = 16 (as each child can be either a boy or a girl)
Number of ways of having only boys in a family = 1 (BBBB)
Number of ways of having only girls in a family = 1 (GGGG)
Number of ways of having no boys in a family = 1 (GGGG)
Number of ways of having no girls in a family = 1 (BBBB)
Number of ways of having at least one boy and one girl in a family = Total number of ways - Number of ways of having only boys - Number of ways of having only girls - Number of ways of having no boys - Number of ways of having no girls
= 16 - 1 - 1 - 1 - 1
= 12
Expected number of families with at least one boy and one girl = Total number of families x probability of having at least one boy and one girl
= 128 x (12/16)
= 96
Therefore, the correct option is (D) 112.
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Out of 128 families with 4 children each, how many are expected to have at least one boy and one girl?a)100.b)105.c)108.d)112.Correct answer is option 'D'. Can you explain this answer?
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Out of 128 families with 4 children each, how many are expected to have at least one boy and one girl?a)100.b)105.c)108.d)112.Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Out of 128 families with 4 children each, how many are expected to have at least one boy and one girl?a)100.b)105.c)108.d)112.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Out of 128 families with 4 children each, how many are expected to have at least one boy and one girl?a)100.b)105.c)108.d)112.Correct answer is option 'D'. Can you explain this answer?.
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