Questions: Giving a test to a group of students, the grades and gender are summarized below A B C Total -------------------------- Male 2 13 18 33 Female 17 5 15 37 Total 19 18 33 70 Answer the following using fractions or decimals rounded to three places. If one student is chosen at random: a. Find the probability that the student received a C in the class. b. Find the probability that the student is a female. c. Find the probability that the student was a male and received a C in the class. d. Find the probability that the student received a B in the class, given they are female. e. Find the probability that the student is a female given they received a B in the class. f. Find the probability that the student is a female and received a B in the class.

$Giving a test to a group of students, the grades and gender are summarized below A B C Total -------------------------- Male 2 13 18 33 Female 17 5 15 37 Total 19 18 33 70 Answer the following using fractions or decimals rounded to three places. If one student is chosen at random: a. Find the probability that the student received a C in the class. b. Find the probability that the student is a female. c. Find the probability that the student was a male and received a C in the class. d. Find the probability that the student received a B in the class, given they are female. e. Find the probability that the student is a female given they received a B in the class. f. Find the probability that the student is a female and received a B in the class.$

Transcript text: Giving a test to a group of students, the grades and gender are summarized below \begin{tabular}{|r|r|r|r|r|} \hline & A & B & C & Total \\ \hline Male & 2 & 13 & 18 & 33 \\ \hline Female & 17 & 5 & 15 & 37 \\ \hline Total & 19 & 18 & 33 & 70 \\ \hline \end{tabular} Answer the following using fractions or decimals rounded to three places. If one student is chosen at random: a. Find the probability that the student received $a(n) C$ in the class. $\square$ b. Find the probability that the student is a female. $\square$ c. Find the probability that the student was a male and received $a(n) C$ in the class. $\square$ d. Find the probability that the student received $a(n) B$ in the class, given they are female. $\square$ e. Find the probability that the student is a female given they received $a(n) B$ in the class. $\square$ f. Find the probability that the student is a female and received a B in the class. $\square$

Solution

Solution Steps

To solve the given probability questions, we will use the data from the table to calculate the probabilities based on the total number of students and the specific conditions given in each question.

a. To find the probability that a student received a C, divide the total number of students who received a C by the total number of students.

b. To find the probability that a student is female, divide the total number of female students by the total number of students.

c. To find the probability that a student is male and received a C, divide the number of male students who received a C by the total number of students.

Step 1: Calculate the Probability of Receiving a C

To find the probability that a randomly chosen student received a C, we use the formula for probability:

\[ P(\text{C}) = \frac{\text{Number of students with C}}{\text{Total number of students}} = \frac{33}{70} \approx 0.4714 \]

Step 2: Calculate the Probability of Being Female

To find the probability that a randomly chosen student is female, we use the formula for probability:

\[ P(\text{Female}) = \frac{\text{Number of female students}}{\text{Total number of students}} = \frac{37}{70} \approx 0.5286 \]

Step 3: Calculate the Probability of Being Male and Receiving a C

To find the probability that a randomly chosen student is male and received a C, we use the formula for probability:

\[ P(\text{Male and C}) = \frac{\text{Number of male students with C}}{\text{Total number of students}} = \frac{18}{70} \approx 0.2571 \]

Final Answer

a. $\boxed{\frac{33}{70}}$

b. $\boxed{\frac{37}{70}}$

c. $\boxed{\frac{18}{70}}$

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