Lincoln High School has 98 teachers. Of the 42 female teachers 8 teach math. One-seventh of all teachers teach math. What is the probability that a teacher is a women or teaches math?
24/49
To find the probability that a teacher is either a woman or teaches math, you need to determine the number of teachers that fall into each category and then use those numbers to calculate the probability.
Step 1: Calculate the number of teachers who are women and teach math.
Given that 8 out of 42 female teachers teach math, there are 8 teachers who are both women and teach math.
Step 2: Calculate the total number of teachers who teach math.
Since one-seventh of all teachers teach math, you can find the total number of teachers who teach math by dividing the total number of teachers by 7.
Total number of teachers who teach math = 98 / 7 = 14 teachers
Step 3: Calculate the number of teachers who are either women or teach math.
To find this number, you need to add the number of female teachers (42) and the number of teachers who teach math (14), but you must subtract the number of teachers who are both women and teach math (8) to avoid double counting.
Number of teachers who are either women or teach math = 42 + 14 - 8 = 48 teachers
Step 4: Calculate the probability.
The probability of a teacher being either a woman or teaching math is the number of teachers who are either women or teach math divided by the total number of teachers.
Probability = Number of teachers who are either women or teach math / Total number of teachers
Probability = 48 / 98
Probability ≈ 0.4898 (rounded to four decimal places) or 48.98% (rounded to the nearest whole percentage)
Therefore, the probability that a teacher at Lincoln High School is either a woman or teaches math is approximately 0.4898 or 48.98%.