A county has 120 bridges, some of which need maintenance. n(A) n(B) Number needi

Question

A county has 120 bridges, some of which need maintenance. n(A) n(B) Number needing road repair n(C) n(AnB) Number needing both painting and road repair n(AnC) Number needing both painting and cable repair: n(BnC) Number needing both road repair and cable repair: 10 Number needing painting: 45 35 30 15 12 Number needing cable repair: n(AnBnc) Number needing painting, road and cable repair: 4 Fill in the numbers in each area of the Venn diagram below, and then answer the questions. (a) How many bridges only require painting? Answer b)How many bridges only require road repair? Answer: (c) What percentage of the bridges require no maintenance? Answer

Explanation / Answer

(a) Number of bridges that require only painting

= n(A) - n(A B) - n(A C) + n(A B C)

= 45 - 15 - 12 + 4

= 22

(b) Number of bridges that require only road repair

= n(B) - n(B A) - n(B C) + n(A B C)

= 35 - 15 - 10 + 4

= 14

(c) Number of bridges that require no maintenance = n(S) - n(A U B U C)

n(A U B U C) = n(A) + n(B) + n(C) - n(A B) - n(B C) - n(A C) + n(A B C)

= 45 + 35 + 30 - 15 - 12 - 10 + 4

= 77

=> Number of bridges that need no maintenace = 120 - 77 = 43

Proportion of bridges that need maintenance = 43/120 = 0.3583

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