Questions: Giving a test to a group of students, the table below summarizes the grade earned by gender. A B C Total ----------------------- Male 12 9 16 37 Female 10 6 13 29 Total 22 15 29 66 If one student is chosen at random, find the probability that the student is female given the student earned grade A. Round your answer to four decimal places.

Giving a test to a group of students, the table below summarizes the grade earned by gender.

A B C Total
-----------------------
Male 12 9 16 37
Female 10 6 13 29
Total 22 15 29 66

If one student is chosen at random, find the probability that the student is female given the student earned grade A. Round your answer to four decimal places.

Transcript text: Giving a test to a group of students, the table below summarizes the grade earned by gender. \begin{tabular}{|r|r|r|r|r|} \hline & A & B & C & Total \\ \hline Male & 12 & 9 & 16 & 37 \\ \hline Female & 10 & 6 & 13 & 29 \\ \hline Total & 22 & 15 & 29 & 66 \\ \hline \end{tabular} If one student is chosen at random, find the probability that the student is female given the student earned grade A. Round your answer to four decimal places. $\square$ Submit Question

Solution

Solution Steps

Step 1: Identify the Event of Interest

The event of interest is: 'Female and A'.

Step 2: Calculate Relevant Totals

Total number of individuals: 66. Count relevant to the event 'Female and A': 10.

Step 3: Calculate the Probability

The probability of 'Female and A' is calculated as: $$P(\text{event}) = \frac{\text{count relevant to the event}}{\text{total number of individuals}} = \frac{10}{66}$$