Solve the problem.
-The faculty at a college consists of 116 full-time teachers and 50 part-time teachers. Of the 116 full-time teachers, 57 are female. Of the 50 part-time teachers, 27 are female. Find the probability that a randomly
Selected teacher is male or works part-time.
A) $\frac { 109 } { 166 }$
B) $\frac { 43 } { 83 }$
C) $\frac { 66 } { 83 }$
D) $\frac { 23 } { 166 }$

Question

Quizplus · Accepted Answer

The total number of teachers is 116 (full-time) + 50 (part-time) = 166. The number of male full-time teachers is 116 - 57 = 59. The number of male part-time teachers is 50 - 27 = 23. So, the total number of male teachers is 59 + 23 = 82. The probability of selecting a male teacher is 82/166. The probability of selecting a part-time teacher (regardless of gender) is 50/166. Since these two groups overlap (male part-time teachers), we subtract the overlap (23/166) to avoid double counting: (82/166 + 50/166) - 23/166 = 109/166.

Solve the Problem 109166\frac { 109 } { 166 }166109​ B) 4383\frac { 43 } { 83 }8343​

Solve the Problem $\frac { 109 } { 166 }$ B) $\frac { 43 } { 83 }$