To determine which contractor Anne should choose based on the likelihood that the job is done on time and on budget, we need to calculate the probabilities for each contractor meeting both conditions.
For Contractor A:
- Probability that the job is done on time = 0.93
- Probability that the job is done within budget = 0.98
The probability that both conditions are met (i.e., the job is done on time and within budget) for Contractor A can be found by multiplying these probabilities together:
[tex]\[ \text{Probability (A)} = 0.93 \times 0.98 = 0.9114 \][/tex]
For Contractor B:
- Probability that the job is done on time = 0.97
- Probability that the job is done within budget = 0.96
Similarly, for Contractor B, the probability that both conditions are met is:
[tex]\[ \text{Probability (B)} = 0.97 \times 0.96 = 0.9312 \][/tex]
Given these calculations:
- Probability that Contractor A meets both conditions = 0.9114
- Probability that Contractor B meets both conditions = 0.9312
To maximize the probability that the job is done on time and on budget, Anne should choose the contractor with the higher probability. In this case, Contractor B has a higher probability (0.9312 compared to 0.9114).
Thus, the correct answer is:
A. Contractor B. The probability that both conditions are met is 0.93.
