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On a survey of 100 boys it was found that 50 used white that 50 used white shirt 40 red and 30 blue. 20 were habituated in using both white and red shirts 15 both red and blue shirts and 10 blue and white shirts. If 10 boys did not use any of the white red or blue colours and 20 boys used all the colours offer your comments.
- a)Inconsistent since 50+40+30-20-15-10+20≠100
- b)Consistent
- c)Cannot determine due to data insufficiency
- d)None
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
On a survey of 100 boys it was found that 50 used white that 50 used w...
Let W be the set of boys using white shirts
Let R be the set of boys using Red shirts.
Let B be the the set of boys using Blue shirts.
GIVEN
n(W) = 50
n(R) = 40
n(B) = 30
n(RUW) = 20
n(RUB) = 15
n(WUB) = 10
n(WUBUR) = 100
TO FIND
n(R∩W∩B) = ?
SOLUTION
By Formula, we know that
n(WURUB)
n(WURUB) =n(W) + n(R) + n(B) - n(WUR) - n(WUB) - n(RUB) + n(R∩W∩B)
Substituting values,
100 = 50 + 40 + 30 - 20 - 15 - 10 + n(R∩W∩B)
=> 100 = 120 - 45 + n(R∩W∩B)
=> n(R∩W∩B) = 100 - 120 + 45
=> n(R∩W∩B) = 145 - 120
=> n(R∩W∩B) = 25
Most Upvoted Answer
On a survey of 100 boys it was found that 50 used white that 50 used w...
B) It is not surprising that some boys did not use any of the colors, as personal preferences and cultural norms vary. The fact that 20 boys used all three colors suggests that they either have a diverse wardrobe or they deliberately chose to rotate between the different colors. It is interesting to note that there is a significant overlap between the different color choices, indicating that boys may not limit themselves to a single color preference.
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On a survey of 100 boys it was found that 50 used white that 50 used white shirt 40 red and 30 blue. 20 were habituated in using both white and red shirts 15 both red and blue shirts and 10 blue and white shirts. If 10 boys did not use any of the white red or blue colours and 20 boys used all the colours offer your comments.a)Inconsistent since 50+40+30-20-15-10+20≠100b)Consistentc)Cannot determine due to data insufficiencyd)NoneCorrect answer is option 'A'. Can you explain this answer?
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