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The directors of the Chatham County School Board consists of 8 Democrats, 3 of whom are female, and 4 Republicans, 2 of whom are female. If a director is chosen at random to discuss an issue on television, what is the probability that the person will be a democrat or female?


1. 6/5
2. 1/6
3. 0
4. 5/6

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Best answer
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) 

\( \frac{8}{{12}} + \frac{5}{{12}} - \frac{3}{{12}} = \frac{{10}}{{12}} = \frac{5}{6}\)

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