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, $55 %$ in
winter 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:

Question

Infinity Learn · Accepted Answer

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∪$$W)$$  $$=90+65+10+7$$−$$55$$−$$8$$−$$6$$−$$4$$−$$4$$−$$3+3+3+2+2$$−$$100=2$$

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