The probabilites that a student will receive an A,B ,C or D grade are 0.4 , 0.3 ,0.2 and 0.1 respectively . Find the probabilty that a stuedent will recive
at most a C grade .

Options

A. `0.3`
B. `0.7`
C. `0.36`
D. none of these

Answer

To find the probability that a student will receive at most a C grade, we need to consider the probabilities of the grades A, B, and C, since "at most a C" means the student can receive either an A, B, or C grade.

### Step-by-Step Solution:

1. **Identify the probabilities of each grade:**
- Probability of receiving an A (P(A)) = 0.4
- Probability of receiving a B (P(B)) = 0.3
- Probability of receiving a C (P(C)) = 0.2
- Probability of receiving a D (P(D)) = 0.1

2. **Determine the grades that fall under "at most a C":**
- The grades that are considered "at most a C" are A, B, and C.

3. **Calculate the total probability of receiving at most a C:**
- To find this, we add the probabilities of receiving A, B, and C:
\[ P(\text{at most C}) = P(A) + P(B) + P(C) \]
\[ P(\text{at most C}) = 0.4 + 0.3 + 0.2 \]

4. **Perform the addition:**
\[ P(\text{at most C}) = 0.4 + 0.3 + 0.2 = 0.9 \]

5. **Conclusion:**
- The probability that a student will receive at most a C grade is **0.9**.