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:

Moderate

Solution

Suppose that number of employee taking vacations is $100$ .
$S u$ – set of employee taking leave in Summer
$W$ – set of employee taking leave in Winter
$S p$ – set of employee taking leave in Spring
$A$ – set of employee taking leave in Autumn
$\begin{array}{l} n (S u) = 90, n (W) = 65, n (S p) = 10, n (A) = 7 \\ n (W \cap S u) = 55, n (S p \cap S u) = 8, n (A \cap S u) = 6 \\ n (W \cap S p) = 4, n (W \cap A u) = 4, n (S p \cap A) = 3 \\ n (S u \cap A) = 3, n (S u \cap W \cap A) = 3 \\ n (S u \cap W \cap S p) = 3, n (S u \cap A \cap S p) = 2 \\ n (W \cap S p \cap A) = 2 \end{array}$
$\begin{array}{l} n (S u \cap S p \cap W \cap A) \\ = n (S u) + n (S p) + n (W) + n (A) - n (S u \cap S p) - n (S p \cap W) - n (W \cap A) - n (S u \cap A) - n (S u \cap W) \\ - n (S p \cap A) + n (S u \cap S p \cap W) + n (S u \cap W \cap A) + n (W \cap A \cap S u) + n (S u \cap S p \cap A) - n (S p \cup S u \cup A \cup W) \end{array}$
$\begin{aligned} = 90 + 65 + 10 + 7 - 55 - 8 - 6 - 4 - 4 - 3 + 3 + 3 + 2 + 2 - 100 = 2 \end{aligned}$

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