To find the probability that a randomly selected student received an A or a B, we need to divide the number of students who received either an A or a B by the total number of students in the class.

Step 1: Total number of students

We can calculate the total number of students by summing all the grades:

$49 \, (A) + 43 \, (B) + 38 \, (C) + 27 \, (D) + 19 \, (F) = 176$

Step 2: Students with A or B

The number of students who received an A or B is:

$49 \, (A) + 43 \, (B) = 92$

Step 3: Probability calculation

The probability that a student received an A or B is the number of A or B students divided by the total number of students:

$P(A \text{ or } B) = \frac{92}{176} \approx 0.5227$

Thus, the probability that a randomly selected student received an A or B is approximately 0.5227.

Would you like further details or have any questions?

Here are 5 related questions to think about:

1. What is the probability that a student received a grade lower than C?
2. What is the probability that a student received a grade of C or better?
3. How would the probability change if the number of A students increased by 10?
4. What is the probability that a randomly selected student received a grade of D or F?
5. How can this method be applied to different types of probability distributions?

Tip: Always ensure the total probability sums to 1 by checking that all grade categories are accounted for.