Answer:
0.1111
Step-by-step explanation:
From the given information;
Number of staffs in the actuary = 80
Out of the 80, 10 are students.
i.e.
P(student actuary) = 10/80 = 0.125
number of weeks in a year = 52
off time per year = 10/52 = 0.1923
P(at work || student actuary) = (50 -10/52)
= 42/52
= 0.8077
P(non student actuary) = (80 -10)/80
= 70 / 80
= 0.875
For a non-student, they are only eligible to 4 weeks off in a year
i.e.
P(at work | non student) = (52-4)/52
= 48/52
= 0.9231
∴
P(at work) = P(student actuary) × P(at work || student actuary) + P(non student actuary) × P(at work || non studnet actuary)
P(at work) = (0.125 × 0.8077) + ( 0.875 × 0.9231)
P(at work) = 0.1009625 + 0.8077125
P(at work) = 0.90868
Finally, the P(he is a student) = (P(student actuary) × P(at work || student actuary) ) ÷ P(at work)
P(he is a student) = (0.125 × 0.8077) ÷ 0.90868
P(he is a student) = 0.1009625 ÷ 0.90868
P(he is a student) = 0.1111
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