Problem 5 (20 Points) John&john plans to launch a new vaccine against the 91-DIVOC. In order to sell the vaccine, it is necessary to receive FDA approval. It costs John&John $500,000 to apply to the FDA. If the FDA approves the vaccine, the profits from the sale of the new vaccine will be $5,000,000. John&John currently estimates that the vaccine will pass the FDA's approval process with a probability of 75%. Suppose that there is another company that is willing to purchase the rights to the vaccine (before John&John applies to the FDA) for $2,000,000. 3/4 Fall 2024 ESI 6325: Applied Probability Methods in Engineering Syllabus John&John has the option to hire Dr. Siddig as a consultant in order to help analyze the vaccine and predict whether it will pass FDA approval. Dr. Siddig charges John&John $200,000 for the consultation fee. They have worked with Dr. Siddig before and have a reasonable understanding of the relationships between his predictions and the FDA approval. In particular, Dr. Siddig is 80% accurate in classifying a successful vaccine (if the vaccine will indeed be approved, 80% of the time he will predict it to be approved). Dr. Siddig is 75% accurate in classifying an unsuccessful vaccine (if the vaccine will indeed be disapproved, 75% of the time he will predict it to be disapproved). Develop and evaluate a decision tree for determining the optimal strategy