Lincoln High School has 98 teachers. Of the 42 female teachers, 8 teach math. One seventh of all of the teachers teach math. What is the probability that a teacher is a man or does not teach math?
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42 of the 98 teachers are female and thus 98 − 42 = 56 98-42=56 98−42=56 of the 98 teachers are male.
To find the probability that a teacher is a man or does not teach math, we need to calculate the number of teachers who are men and/or do not teach math, and then divide it by the total number of teachers.
Let's break down the information given:
- Total number of teachers at Lincoln High School = 98
- Number of female teachers = 42
- Number of female math teachers = 8
- One-seventh of all teachers teach math
To find the number of male teachers, we subtract the number of female teachers from the total number of teachers:
Number of male teachers = Total number of teachers - Number of female teachers
= 98 - 42
= 56
Since one-seventh of all teachers teach math, we can calculate the total number of math teachers:
Total number of math teachers = (1/7) * Total number of teachers
= (1/7) * 98
= 14
Now, let's find the number of teachers who are men and/or do not teach math. We'll add together the number of male teachers and the number of teachers who do not teach math.
Number of teachers who are men and/or do not teach math = Number of male teachers + (Total number of teachers - Total number of math teachers)
= 56 + (98 - 14)
= 56 + 84
= 140
Finally, we can calculate the probability that a teacher is a man or does not teach math by dividing the number of teachers who are men and/or do not teach math by the total number of teachers:
Probability = Number of teachers who are men and/or do not teach math / Total number of teachers
= 140 / 98
= 10/7 (approximately 1.43)
Therefore, the probability that a teacher is a man or does not teach math is approximately 1.43.
no of maths teachers:98/7=14
no of male maths teachers:14-8=6
no of male teachers:98-42=56
no male teachers who do not teach maths:56-6=50