The probability that Sunil will recelve a D in is matchematics course is 0.61 and the probability that he will receive a C is 0.28. What is the probability tat Sunil will receive a C or D in mathematics ?

Answer

To solve the problem step by step, we will follow the principles of probability.

### Step 1: Identify the given probabilities
We are given:
- Probability of receiving a D, \( P(D) = 0.61 \)
- Probability of receiving a C, \( P(C) = 0.28 \)

### Step 2: Understand the requirement
We need to find the probability that Sunil will receive either a C or a D in mathematics. This can be expressed in probability notation as \( P(C \cup D) \), which represents the union of events C and D.

### Step 3: Use the formula for the union of two events
The formula for the probability of the union of two events is:
\[ P(C \cup D) = P(C) + P(D) - P(C \cap D) \]
where \( P(C \cap D) \) is the probability that both events occur simultaneously.

### Step 4: Determine if events C and D are mutually exclusive
Since receiving a C and receiving a D are mutually exclusive events (one cannot receive both a C and a D at the same time), we have:
\[ P(C \cap D) = 0 \]

### Step 5: Substitute the values into the formula
Now we can substitute the known values into the formula:
\[ P(C \cup D) = P(C) + P(D) - P(C \cap D) \]
\[ P(C \cup D) = 0.28 + 0.61 - 0 \]

### Step 6: Calculate the result
Now we perform the addition:
\[ P(C \cup D) = 0.28 + 0.61 = 0.89 \]

### Conclusion
Thus, the probability that Sunil will receive either a C or a D in mathematics is:
\[ P(C \cup D) = 0.89 \]

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