To determine the probability that a randomly chosen student received a grade of C, we need to follow these steps:
1. Count the Total Number of Students:
We sum up the number of students in each category (A, B, and C) for both males and females.
- Number of male students who got an A: [tex]\(4\)[/tex]
- Number of male students who got a B: [tex]\(9\)[/tex]
- Number of male students who got a C: [tex]\(17\)[/tex]
- Number of female students who got an A: [tex]\(5\)[/tex]
- Number of female students who got a B: [tex]\(11\)[/tex]
- Number of female students who got a C: [tex]\(19\)[/tex]
Therefore, the total number of students is:
[tex]\[
4 + 9 + 17 + 5 + 11 + 19 = 65
\][/tex]
2. Count the Number of Students who got a C:
We sum up the number of students who received a C for both genders.
- Number of males who got a C: [tex]\(17\)[/tex]
- Number of females who got a C: [tex]\(19\)[/tex]
Therefore, the total number of students who got a C is:
[tex]\[
17 + 19 = 36
\][/tex]
3. Calculate the Probability:
The probability of a randomly chosen student getting a C is given by the ratio of the number of students who got a C to the total number of students.
[tex]\[
\text{Probability} = \frac{\text{Number of students who got a C}}{\text{Total number of students}} = \frac{36}{65}
\][/tex]
4. Round the Probability to Four Decimal Places:
The exact probability comes out to approximately [tex]\(0.5538461538461539\)[/tex]. When we round this value to four decimal places, we get:
[tex]\[
\text{Probability} \approx 0.5538
\][/tex]
Therefore, the probability that a randomly chosen student received a grade of C is [tex]\(0.5538\)[/tex] when rounded to four decimal places.
