Given the following test grades and gender summary:

\begin{tabular}{|r|r|r|r|r|}
\hline & A & B & C & Total \\
\hline Male & 20 & 13 & 5 & 38 \\
\hline Female & 2 & 14 & 8 & 24 \\
\hline Total & 22 & 27 & 13 & 62 \\
\hline
\end{tabular}

If one student is chosen at random, find the probability that the student got an A or a B on the test. Write your answer as a reduced fraction or whole number.

[tex]\[ P(A \text{ or } B)= \][/tex]

[tex]\[\square\][/tex]



Answer :

To determine the probability that a randomly chosen student from this group received either an A or a B on the test, follow these steps:

1. Identify and sum the total number of students who received an A.
2. Identify and sum the total number of students who received a B.
3. Add these two sums together to get the number of students who received either an A or a B.
4. Divide the number of students who received an A or a B by the total number of students to find the probability.

Given data:
- Total number of students: [tex]\( 62 \)[/tex]
- Number of students who got an A: [tex]\( 22 \)[/tex]
- Number of students who got a B: [tex]\( 27 \)[/tex]

Step-by-step solution:
1. Number of students who got an A: [tex]\( 22 \)[/tex]
2. Number of students who got a B: [tex]\( 27 \)[/tex]
3. Number of students who got either an A or a B:
[tex]\[ 22 + 27 = 49 \][/tex]
4. Probability of a student getting an A or a B:
[tex]\[ \frac{\text{Number of students who got either an A or a B}}{\text{Total number of students}} = \frac{49}{62} \][/tex]

So, the probability that a randomly chosen student got an A or a B is:
[tex]\[ P(A \text { or } B) = \frac{49}{62} \][/tex]