Correct Answer - Option 4 : 5/6
Concept:
- For two events A and B, we have: P(A ∪ B) = P(A or B) = P(A) + P(B) - P(A ∩ B).
Calculation:
There are 12 directors, of whom 8 are Democrats and 5 are female. But 3 of the directors are Democrats and females, and cannot be counted twice.
Let P(D) = Probability that the person will be a democrat = 8/12
P(F) = Probability that the person will be a female = 5/12
P(D ∩ F) = Probability that the person will be democrats and females = 3/12
Probability that the person will be a democrat or female = P(D ∪ F)
= P(D) + P(F) - P(D ∩ F)
= \( \frac{8}{{12}} + \frac{5}{{12}} - \frac{3}{{12}} = \frac{{10}}{{12}} = \frac{5}{6}\)