The probabilities 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 probability that a student will receive B or C grade.

Options

A. A. 0.2
B. B. 0.5
C. C. 0.8
D. D. 0.6

Answer

To find the probability that a student will receive a B or C grade, we can follow these steps:

### Step 1: Identify the probabilities given in the question.
The probabilities for each grade are:
- Probability of receiving an A grade (P(A)) = 0.4
- Probability of receiving a B grade (P(B)) = 0.3
- Probability of receiving a C grade (P(C)) = 0.2
- Probability of receiving a D grade (P(D)) = 0.1

### Step 2: Write down the probabilities for B and C.
From the information provided:
- P(B) = 0.3
- P(C) = 0.2

### Step 3: Calculate the probability of receiving either a B or C grade.
To find the probability of receiving a B or C grade, we can use the addition rule of probabilities. Since B and C are mutually exclusive events (a student cannot receive both grades at the same time), we can simply add their probabilities:
\[ P(B \text{ or } C) = P(B) + P(C) \]

### Step 4: Substitute the values into the equation.
Now we substitute the values we have:
\[ P(B \text{ or } C) = P(B) + P(C) = 0.3 + 0.2 \]

### Step 5: Perform the addition.
Calculating the sum:
\[ P(B \text{ or } C) = 0.3 + 0.2 = 0.5 \]

### Step 6: State the final answer.
Thus, the probability that a student will receive a B or C grade is:
\[ P(B \text{ or } C) = 0.5 \]