If the probability that Mike will miss at least one of ten jobs assigned to him is 0.55, then what is the probability that he will do all ten jobs?

Options

A. 0.1
B. 0.45
C. 0.55
D. 0.85

Answer

To solve the problem, we need to find the probability that Mike will do all ten jobs, given that the probability he will miss at least one job is 0.55.

### Step-by-Step Solution:

1. **Understand the Problem**: We are given that the probability of Mike missing at least one job is 0.55. We need to find the probability that he will complete all ten jobs.

2. **Define Probabilities**:
- Let \( P(A) \) be the probability that Mike does all jobs.
- Let \( P(B) \) be the probability that Mike misses at least one job.

3. **Relationship Between Probabilities**:
- The events "Mike does all jobs" and "Mike misses at least one job" are complementary events. This means that if Mike does all jobs, he cannot miss any job, and vice versa.
- Therefore, we can express this relationship as:
\[ P(A) + P(B) = 1 \]

4. **Substituting the Given Probability**:
- We know from the problem that \( P(B) = 0.55 \).
- Substituting this into the equation gives us:
\[ P(A) + 0.55 = 1 \]

5. **Solving for \( P(A) \)**:
- Rearranging the equation to solve for \( P(A) \):
\[ P(A) = 1 - 0.55 \]
\[ P(A) = 0.45 \]

6. **Conclusion**:
- The probability that Mike will do all ten jobs is \( 0.45 \).

### Final Answer:
The probability that Mike will do all ten jobs is **0.45**.

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