Question
Asked Oct 30, 2019
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A survey of 400 people shows that 102 people like red, 100- blue, 100 -green, 56- orange , 48 yellow and 40 violet. 30 like both red and blue , 37 - red and green , 39 - blue and green, 20 -orange and yellow, 18 - orange and violet and 22 - yellow and violet. However 90 of them like none. IN addition number of people who like (red and blue and green) is 5 times those who like (yellow and orange and violet). 

a) Represent in a venn diagram

B) Find people who like one colour

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Expert Answer

Step 1

Let number of people who like yellow and orange and violet be x.

Then number of people who like red and blue and green = 5x

Use the concept of probability of union of three or more set

Let “r” denotes red, “g” denotes green, “b” denotes blue, “o” denotes orange, “y” denotes yellow and “v” denotes violet.

Then

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400 P(rbug)+P(vUoUy)+90 and P(rbug)P(r) P (b) + P (g) - P(bng)- P(rng)-P(rob) +P(robng) P(you)P(y)+ P(o)+ P(v)-P(yno)-P(onv)-P(yov) +P(ynonv)

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Step 2

Let

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P(ynonv)x then P(rnbng)= 5x so 400 102 100+100-30 -37-39+5x + 48+ 56 +40 -20-18-22+x +90 120 90 6x 30 6x x =5 Hence P(ynonv) 5 and P(rnbng)25

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Step 3

The Venn diagram...

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400 (total) 102(red) 48(yellow) 56(orange) 100(green) 25 100(blue) 40(violet) 90(none)

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