Question

Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects. One method of increasing​ patients' awareness of the problem is for physicians to provide patient medication instruction​ (PMI) sheets. A local medical​ survey, however, has found that only 31​% of the doctors who prescribe drugs frequently distribute PMI sheets to their patients. Assume that 31​% of all patients receive the PMI sheet with their prescriptions and that 18​% receive the PMI sheet and are hospitalized because of a​drug-related problem. What is the probability that a person will be hospitalized for a​ drug-related problem given that the person received the PMI​ sheet?

Answer 1

The probability that a person will be hospitalized for a drug-related problem given that the person received the PMI sheet is 0.5806.

Step-by-step explanation:

To find the probability that a person will be hospitalized for a drug-related problem given that the person received the PMI sheet, we can use conditional probability. Conditional probability is the probability of an event occurring given that another event has already occurred.

In this case, the probability of being hospitalized for a drug-related problem given that the person received the PMI sheet is denoted as P(Hospitalized | PMI). We are given that 18% of patients receive the PMI sheet and are hospitalized for a drug-related problem, so the probability of receiving the PMI sheet and being hospitalized is 0.18.

The formula for conditional probability is P(A | B) = P(A and B) / P(B). In this case, A represents being hospitalized and B represents receiving the PMI sheet. So we have:

P(Hospitalized | PMI) = P(Hospitalized and PMI) / P(PMI)

Substituting the given values, we have:

P(Hospitalized | PMI) = 0.18 / 0.31 = 0.5806 (rounded to four decimal places)