Among employee of a company taking vacations last years, 90% took vacations in the summer, 65% in the winter, 10% in the spring, 7% in the autumn, 55% inwinter and summer, 8% in the spring and summer, 6% in the autumn and summer, 4% in the winter and spring, 4% in winter and autumn, 3% in the spring and autumn, 3% in the summer, winter and spring, 3% in the summer, winter and autumn, 2% in the summer, autumn and spring, and 2% in the winter, spring and autumn. Percentage of employee that took vacations during every season:
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a
4
b
3
c
2
d
8
answer is C.
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Detailed Solution
Suppose that number of employee taking vacations is 100.Su – set of employee taking leave in SummerW – set of employee taking leave in WinterSp – set of employee taking leave in SpringA – set of employee taking leave in Autumnn(Su)=90,n(W)=65,n(Sp)=10,n(A)=7n(W∩Su)=55,n(Sp∩Su)=8,n(A∩Su)=6n(W∩Sp)=4,n(W∩Au)=4,n(Sp∩A)=3n(Su∩A)=3,n(Su∩W∩A)=3n(Su∩W∩Sp)=3,n(Su∩A∩Sp)=2n(W∩Sp∩A)=2n(Su∩Sp∩W∩A)=n(Su)+n(Sp)+n(W)+n(A)−n(Su∩Sp)−n(Sp∩W)−n(W∩A)−n(Su∩A)−n(Su∩W) −n(Sp∩A)+n(Su∩Sp∩W)+n(Su∩W∩A)+n(W∩A∩Su)+n(Su∩Sp∩A)−n(Sp∪Su∪A∪W) =90+65+10+7−55−8−6−4−4−3+3+3+2+2−100=2