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

To find the probability that the construction job will be completed on time, we can use the law of total probability. We have two scenarios: one where there is a strike and one where there isn't.

Given Information

• Probability of a strike (P(Strike)) = 0.65
• Probability of no strike (P(No Strike)) = 1 - P(Strike) = 0.35
• Probability of completing on time if there is no strike (P(On Time | No Strike)) = 0.80
• Probability of completing on time if there is a strike (P(On Time | Strike)) = 0.32

Calculating Total Probability

The total probability of completing the job on time (P(On Time)) can be calculated as follows:

P(On Time) = P(On Time | No Strike) * P(No Strike) + P(On Time | Strike) * P(Strike)

Substituting the values:

P(On Time) = (0.80 * 0.35) + (0.32 * 0.65)

Now, let's do the calculations:

• 0.80 * 0.35 = 0.28
• 0.32 * 0.65 = 0.208

Adding these results together:

P(On Time) = 0.28 + 0.208 = 0.488

Final Result

The probability that the construction job will be completed on time is 0.488, or 48.8%.