A person has undertaken a construction job. The probablities are 0.65 that will be strike, 0.80 that the construction job will becompleted on time if there is no strike, and 0.32 that the construction job will be completed on time if there is a strike. Then the probability that the construction job will be completed on time is

Options

A. `0 . 788`
B. `0 . 488`
C. `1 . 488`
D. `1.634`

Answer

To find the probability that the construction job will be completed on time, we can use the law of total probability. We will consider two scenarios: when there is a strike and when there is no strike.

### Step-by-step Solution:

1. **Identify Given Probabilities:**
- Probability of strike (P(S)) = 0.65
- Probability of no strike (P(S')) = 1 - P(S) = 1 - 0.65 = 0.35
- Probability of completing the job on time if there is a strike (P(C|S)) = 0.32
- Probability of completing the job on time if there is no strike (P(C|S')) = 0.80

2. **Apply the Law of Total Probability:**
The total probability of completing the job on time (P(C)) can be calculated as:
\[ P(C) = P(S) \cdot P(C|S) + P(S') \cdot P(C|S') \]

3. **Substitute the Values:**
\[ P(C) = (0.65 \cdot 0.32) + (0.35 \cdot 0.80) \]

4. **Calculate Each Term:**
- Calculate \(0.65 \cdot 0.32\):
\[ 0.65 \cdot 0.32 = 0.208 \]
- Calculate \(0.35 \cdot 0.80\):
\[ 0.35 \cdot 0.80 = 0.28 \]

5. **Add the Results:**
\[ P(C) = 0.208 + 0.28 = 0.488 \]

6. **Final Result:**
The probability that the construction job will be completed on time is:
\[ P(C) = 0.488 \]