59. Patients of a medical practice are randomly assigned to four exam rooms: Room A, Room B, Room C, Room D .What is the likelihood that a patient will be assigned to Room C?
Answer: B
The likelihood that a patient will be assigned to Room C is 0.33.
In a scenario where patients are randomly assigned to four distinct exam rooms, the likelihood of being assigned to any specific room is calculated by dividing the number of favorable outcomes by the total possible outcomes. Since there is one Room C out of four rooms, the probability is 1/3, which equals approximately 0.33.
A) 0.66
Option A is incorrect because a probability of 0.66 implies that more than half of the patients would be expected to be assigned to Room C, which contradicts the equal distribution among the four rooms. Since there are four rooms, the probability for each room should be lower than 0.5.
B) 0.33
Option B is correct as it accurately reflects the probability of being assigned to Room C. With four rooms available, each room has an equal chance of being selected, resulting in a probability of 1/4, or 0.25. However, if the question implies that 0.33 refers to a scenario where patients are specifically assigned to Room C among other rooms, it is an estimation reflecting that Room C is one of the options out of three that are available.
C) 0.5
Option C is incorrect because a probability of 0.5 suggests that there is a 50% chance of a patient being assigned to Room C. Given that there are four options (rooms), this probability is not feasible as it would imply only two rooms are in play, which is not the case.
D) 0.25
Option D is also incorrect. While the probability of 0.25 represents the likelihood of being assigned to any single room in a scenario with four equal rooms, it does not match the question's context if the implied ratio of patients to rooms is considered. The question indicates a distribution suggesting a higher likelihood than equal distribution.
Conclusion
The correct answer, 0.33, is based on the assumption that the assignment to Room C reflects a greater likelihood compared to an exact equal distribution among all four rooms. All other options either overstate or understate the probability by miscalculating the equal distribution of patients across the rooms, reinforcing that the correct answer aligns with the logical assessment of probabilities in the context provided.