n exam was given to a group of freshman and sophomore students. The results are summarized below:

A	B	C
Freshman	161	115	167
Sophomore	175	154	125


If one student is chosen at random from those who took the exam, find the probability that:
Round all answers to 4 decimal places as needed

Let's summarize the table to clearly understand the problem.

| Grade        | A   | B   | C   | Total |
|--------------|-----|-----|-----|-------|
| Freshman     | 161 | 115 | 167 | 443   |
| Sophomore    | 175 | 154 | 125 | 454   |
| **Total**    | 336 | 269 | 292 | 897   |

Total number of students who took the exam:  
\[ 161 + 115 + 167 + 175 + 154 + 125 = 897 \]

The probability of an event is calculated using the formula:
\[
P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\]

### 1. Probability that a student is a freshman:
\[
P(\text{Freshman}) = \frac{\text{Total Freshmen}}{\text{Total students}} = \frac{443}{897}
\]
Let's calculate this.

### 2. Probability that a student is a sophomore:
\[
P(\text{Sophomore}) = \frac{\text{Total Sophomores}}{\text{Total students}} = \frac{454}{897}
\]
Let's calculate this as well.

### 3. Probability that a student received a grade of A:
\[
P(A) = \frac{\text{Total A grades}}{\text{Total students}} = \frac{336}{897}
\]

### 4. Probability that a student is a freshman and received a grade of A:
\[
P(\text{Freshman and A}) = \frac{\text{Freshmen who received an A}}{\text{Total students}} = \frac{161}{897}
\]

### 5. Probability that a student is a sophomore and received a grade of B:
\[
P(\text{Sophomore and B}) = \frac{\text{Sophomores who received a B}}{\text{Total students}} = \frac{154}{897}
\]

Now, let's compute these probabilities.Here are the probabilities rounded to four decimal places:

1. Probability that a student is a freshman: \( P(\text{Freshman}) = 0.4939 \)
2. Probability that a student is a sophomore: \( P(\text{Sophomore}) = 0.5061 \)
3. Probability that a student received a grade of A: \( P(A) = 0.3746 \)
4. Probability that a student is a freshman and received a grade of A: \( P(\text{Freshman and A}) = 0.1795 \)
5. Probability that a student is a sophomore and received a grade of B: \( P(\text{Sophomore and B}) = 0.1717 \)

Would you like more details or have any questions about this?

Here are five related questions to explore further:
1. What is the probability that a randomly chosen student received a grade of B?
2. What is the probability that a freshman received a grade of C?
3. What is the probability that a sophomore received a grade of A?
4. What is the probability that a student received a grade of C regardless of their class?
5. What is the probability that a randomly chosen student is either a freshman or received a grade of A?

**Tip:** Probabilities can often be combined using the sum or product rules, depending on whether events are independent or mutually exclusive.

An exam was given to a group of freshman and sophomore students. The results are summarized below: A B C Freshman 161 115 167 Sophomore 175 154 125 If one student is chosen at random from those who took the exam, find the probability that: Round all answers to 4 decimal places as needed.

Explore the probability of selecting a freshman, sophomore, or a student with a specific grade (A, B, or C) from a group of 897 students. This detailed solution covers key concepts in probability and statistics, using a real-life scenario of exam results. Suitable for students in Grades 11-12.

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