Lecture 13 Bernoulli’s Formula. The Most Probable Number of Occurrences of an Event If n

Using the total probability formula, we obtain



Example 4. The hospital receives an average of 50% of patients with the disease F, 30% of patients with the disease L, and 20% of patients with the disease C. The probability that the patient will completely recovered from the illness F is equal to 0.7; for the illnesses L and C, these probabilities are equal to 0.8 and 0.9, respectively. The patient admitted to the hospital was discharged healthy. Find the probability that the patient was suffering from the disease F.

Solution. If follows from the hypothesis that



where is the probability of the fact that the patient in the hospital is suffering from the disease F. The probabilities and are defined similarly. Let A be the event that the patient admitted to the hospital was discharged healthy.

It is clear that

.

Now using the total probability formula, we obtain



Therefore, the desired probability (i.e. the probability of the fact that the patient that had been discharged was suffering from the disease F) can be found from the Bayes formula

.