To find the probability that a randomly chosen student was either female or got a "B" grade, we need to count the total number of students who meet at least one of these criteria and then divide by the total number of students.
Here's a step-by-step solution:
1. Total number of students: According to the table, the total number of students is 71.
2. Total number of females: There are 34 female students.
3. Total number of "B" grades: There are 35 students who received a "B" grade.
4. Number of females who received a "B": From the table, we see that there are 19 female students who received a "B" grade.
5. Using the principle of inclusion and exclusion: To avoid double-counting students who are both female and received a "B" grade, we use the following formula:
[tex]\[
\text{Total females or B} = (\text{Total females}) + (\text{Total B grades}) - (\text{Number of females who received a B})
\][/tex]
Plugging in the numbers:
[tex]\[
\text{Total females or B} = 34 + 35 - 19 = 50
\][/tex]
6. Calculate the probability: The probability is determined by dividing the total number of students who are either female or received a "B" by the total number of students:
[tex]\[
\text{Probability} = \frac{\text{Total females or B}}{\text{Total students}} = \frac{50}{71}
\][/tex]
7. Simplify the result: The probability as a decimal is approximately 0.7042.
So, the probability that a randomly chosen student was either female or received a "B" grade is [tex]\( \frac{50}{71} \)[/tex] or approximately 0.7042.
