Problem

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 & 6 & 11 & 15 & 32 \\
\hline Female & 9 & 19 & 20 & 48 \\
\hline Total & 15 & 30 & 35 & 80 \\
\hline
\end{tabular}
If one student is chosen at random,
Find the probability that the student was female AND got a "A".

Answer

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Answer

Final Answer: The probability that the student was female and got an 'A' is \(\boxed{0.1125}\).

Steps

Step 1 :The problem provides a table summarizing the grades and gender of a group of students. The table is as follows: \begin{tabular}{|r|r|r|r|r|} \hline & A & B & C & Total \\ \hline Male & 6 & 11 & 15 & 32 \\ \hline Female & 9 & 19 & 20 & 48 \\ \hline Total & 15 & 30 & 35 & 80 \\ \hline \end{tabular}

Step 2 :We are asked to find the probability that a student chosen at random is female and got an 'A'.

Step 3 :The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes.

Step 4 :In this case, the event is a student being female and getting an 'A'. The number of ways this can occur is the number of female students who got an 'A', which is 9.

Step 5 :The total number of outcomes is the total number of students, which is 80.

Step 6 :So, the probability is \(\frac{9}{80}\).

Step 7 :Final Answer: The probability that the student was female and got an 'A' is \(\boxed{0.1125}\).

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