Answered

Given the grades and gender summary below, find the probability that a student chosen at random is male OR received a "B".

\begin{tabular}{|r|r|r|r|r|}
\hline & A & B & C & Total \\
\hline Male & 19 & 14 & 9 & 42 \\
\hline Female & 17 & 15 & 2 & 34 \\
\hline Total & 36 & 29 & 11 & 76 \\
\hline
\end{tabular}

If one student is chosen at random,
Find the probability that the student was male OR got a "B".



Answer :

GinnyAnswer
To solve the problem of finding the probability that a randomly chosen student was either male or got a "B" (or both), we can use the concepts of probability and the principles of set theory. Here is a detailed step-by-step solution:

### Given Data:
1. Total number of students: [tex]\( 76 \)[/tex]
2. Number of male students: [tex]\( 42 \)[/tex]
3. Number of students who got a "B": [tex]\( 29 \)[/tex]
4. Number of male students who got a "B": [tex]\( 14 \)[/tex]

### Step-by-Step Solution:

Step 1: Calculate the probability of a student being male.
[tex]\[ \text{Probability of being male} = \frac{\text{Number of male students}}{\text{Total number of students}} = \frac{42}{76} \][/tex]
[tex]\[ \text{Probability of being male} = 0.5526315789473685 \][/tex]

Step 2: Calculate the probability of a student getting a "B."
[tex]\[ \text{Probability of getting a "B"} = \frac{\text{Number of students who got a "B"}}{\text{Total number of students}} = \frac{29}{76} \][/tex]
[tex]\[ \text{Probability of getting a "B"} = 0.3815789473684211 \][/tex]

Step 3: Calculate the probability of a student being both male and getting a "B."
[tex]\[ \text{Probability of being male and getting a "B"} = \frac{\text{Number of male students who got a "B"}}{\text{Total number of students}} = \frac{14}{76} \][/tex]
[tex]\[ \text{Probability of being male and getting a "B"} = 0.18421052631578946 \][/tex]

Step 4: Use the formula for the probability of the union of two events (Male ∪ B):
[tex]\[ \text{Probability of (Male OR B)} = \text{Probability of (Male)} + \text{Probability of (B)} - \text{Probability of (Male AND B)} \][/tex]
[tex]\[ \text{Probability of (Male OR B)} = 0.5526315789473685 + 0.3815789473684211 - 0.18421052631578946 \][/tex]
[tex]\[ \text{Probability of (Male OR B)} = 0.7500000000000001 \][/tex]

### Conclusion:
The probability that a randomly chosen student was either male or got a "B" is [tex]\( 0.7500000000000001 \)[/tex] or [tex]\( 75\% \)[/tex].