Juliana estimates that there's a 50% probability that the construction of her company's new data storage facility will be completed within the next month.However, she believes that it is 30% likely that the construction will take two months, and 20% likely it will take a full three months.She also believes that if the construction is completed within one month, there is a 65% likelihood that she can have the facility fully staffed and operational by summer.If the construction takes two months, the chances of meeting the summer deadline drops to 40%; and if the construction takes three months, there is only a 10% probability meeting the summer deadline.How likely is it that Juliana will not meet the summer deadline?
A).200
B).346
C).685
D).282
E).535

Question

Quizplus · Accepted Answer

To calculate the probability of not meeting the summer deadline, we first find the probability of meeting the deadline under each construction timeline and then subtract these from 1 to find the probability of not meeting the deadline. Finally, we sum these probabilities weighted by the likelihood of each construction timeline.1. If completed in 1 month: $0.50 \times 0.65 = 0.325$ chance of meeting the deadline, so $0.50 - 0.325 = 0.175$ chance of not meeting it.2. If completed in 2 months: $0.30 \times 0.40 = 0.12$ chance of meeting the deadline, so $0.30 - 0.12 = 0.18$ chance of not meeting it.3. If completed in 3 months: $0.20 \times 0.10 = 0.02$ chance of meeting the deadline, so $0.20 - 0.02 = 0.18$ chance of not meeting it.Adding these probabilities gives the total probability of not meeting the summer deadline: $0.175 + 0.18 + 0.18 = 0.535$ or 53.5%.

Juliana Estimates That There's a 50% Probability That the Construction