The faculty
Probability
Level
2
A school had 8 female and 4 male English teachers, 10 male and 5 female Science teachers, and 6 female and 3 male Arts teachers.
If you pick a department at random, and then pick a teacher from that department at random, what is the chance you pick a female teacher?
1/2
5/9
19/36
2/3
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1 solution
The chance of picking the English department is 1/3. If you do, the chance of picking a female teacher from the English department is 2/3. So the probability of a female teacher from the English dept. is 1/3 * 2/3 = 2/9.
The probability of a female teacher from the Science department is 1/3 * 1/3 = 1/9.
The probability of a female teacher from the Arts department is 1/3 * 2/3 = 2/9.
Add them up, and the total probability of a female teacher from any of the three departments is 2/9 + 1/9 + 2/9 = 5/9.