Question

question 2 of 10
anne is choosing a contractor. she has narrowed down her selection to two companies and will base her decision on the likelihood that the job is done on time and on budget. she uses online reviews to estimate the probabilities.

	contractor a	contractor b
probability that the job is done within budget	0.98	0.96

which contractor should anne choose to maximize the probability that the job will be done on time and on budget? assume all events are independent.

a. contractor b. the probability that both conditions are met is 0.93.

b. contractor a. the probability that both conditions are met is 0.91.

c. contractor b. the probability that both conditions are met is 0.97.

d. contractor a. the probability that both conditions are met is 0.98.

Explanation:

Step1: Recall independent events formula

For independent events, \( P(A \cap B) = P(A) \times P(B) \). We'll calculate this for both contractors.

Step2: Calculate for Contractor A

Let \( P(\text{on time}) = 0.93 \), \( P(\text{on budget}) = 0.98 \).
\( P(\text{both}) = 0.93 \times 0.98 = 0.9114 \approx 0.91 \) (rounded appropriately).

Step3: Calculate for Contractor B

Let \( P(\text{on time}) = 0.97 \), \( P(\text{on budget}) = 0.96 \).
\( P(\text{both}) = 0.97 \times 0.96 = 0.9312 \approx 0.93 \) (but wait, let's check options. Wait, no—wait, the options: Wait, option B says Contractor A with 0.91, which matches our calculation for A (0.9114 ≈ 0.91). Wait, but wait, did I miscalculate? Wait, 0.930.98: 0.930.98 = (0.9 + 0.03)(0.9 + 0.08) = 0.81 + 0.072 + 0.027 + 0.0024 = 0.9114. Yes. For B: 0.97*0.96 = (1 - 0.03)(1 - 0.04) = 1 - 0.07 + 0.0012 = 0.9312. But the options: Option A says Contractor B with 0.93 (close to 0.9312), but wait the options: Wait the original options:

A. Contractor B. The probability... is 0.93.
B. Contractor A. The probability... is 0.91.
C. Contractor B. The probability... is 0.97.
D. Contractor A. The probability... is 0.98.

Wait, our calculation for A is ~0.91, for B is ~0.93. So which is higher? 0.9312 > 0.9114, so Contractor B has higher probability. But wait, option A says Contractor B with 0.93 (which is approximate 0.9312). But wait, let's check the options again. Wait, maybe I made a mistake. Wait, the problem says "maximize the probability". So Contractor B's probability is ~0.93, Contractor A's is ~0.91. So the correct option should be A? Wait no—wait, option A: "Contractor B. The probability that both conditions are met is 0.93." Which is correct (0.9312 ≈ 0.93). But wait, the options: Wait, let's re-express:

Wait, my calculation for A: 0.93*0.98 = 0.9114 ≈ 0.91 (matches option B).
For B: 0.97*0.96 = 0.9312 ≈ 0.93 (matches option A).

So since 0.9312 > 0.9114, Contractor B has higher probability. So option A says Contractor B with 0.93, which is correct. Wait, but the options: Let's check the options again:

A. Contractor B. The probability that both conditions are met is 0.93.
B. Contractor A. The probability that both conditions are met is 0.91.
C. Contractor B. The probability that both conditions are met is 0.97.
D. Contractor A. The probability that both conditions are met is 0.98.

So 0.9312 is approximately 0.93, so option A is correct. Wait, but earlier I thought maybe I messed up, but no—Contractor B's probability is higher. So the correct answer is A. Wait, but let's confirm:

Contractor A: 0.93 * 0.98 = 0.9114 ≈ 0.91
Contractor B: 0.97 * 0.96 = 0.9312 ≈ 0.93

Since 0.93 > 0.91, Anne should choose Contractor B, with probability ~0.93, which is option A.

Answer:

A. Contractor B. The probability that both conditions are met is 0.93.