Final answer:
The probability that the construction job will be completed on time, considering the probabilities of a strike and on-time completion in both scenarios, is 0.55 or 55%.
Step-by-step explanation:
The question you've asked is about calculating the probability that a construction job will be completed on time, given the chance of a strike and the probabilities of on-time completion contingent upon whether a strike occurs or not. The probabilities provided are:
- Probability of a strike (P(S)): 0.60
- Probability of on-time completion given no strike (P(On time | No strike)): 0.85
- Probability of on-time completion given a strike (P(On time | Strike)): 0.35
To find the total probability of the construction job being completed on time, we use the law of total probability:
P(On time) = P(No strike) × P(On time | No strike) + P(Strike) × P(On time | Strike)
First, we need to calculate the probability of no strike occurring, which is the complement of the probability of a strike:
P(No strike) = 1 - P(Strike) = 1 - 0.60 = 0.40
Now we can calculate the overall probability:
P(On time) = 0.40 × 0.85 + 0.60 × 0.35 = 0.34 + 0.21 = 0.55
Therefore, the probability that the construction job will be completed on time is 0.55 or 55%.