63. A hospital's root cause analysis annual summary shows that 35% of the root causes are due to leadership (L) and 15% are due to communication (C). Of those due to leadership (L), there is a 10% chance they are also due to communication (C). What is the probability (P) that a root cause is due to leadership (L) given a root cause of communication (C)?
Answer: A
P (L|C)
To find the probability that a root cause is due to leadership (L) given that it is also due to communication (C), we denote this as P(L|C). This probability is calculated using the information provided in the summary, which indicates the relationships between leadership and communication in root causes.
A) P (L|C)
This option is correct as it directly represents the probability we are trying to calculate: the likelihood that a root cause is due to leadership given that it is due to communication.
B) P (C or L)
This option is incorrect because it refers to the probability that a root cause is due to either communication or leadership, not specifically the conditional probability of leadership given communication.
C) P (C and L)
This option is incorrect as it denotes the joint probability that a root cause is due to both communication and leadership. While it is related, it does not provide the conditional probability we are looking for.
D) P (C|L)
This option is incorrect because it represents the probability that a root cause is due to communication given that it is due to leadership. This is the inverse of what is being asked in the question.
Conclusion
The correct answer, P(L|C), accurately defines the conditional probability we need to calculate based on the relationship between leadership and communication as root causes. All other options misinterpret the nature of the probability being requested, focusing on either joint probabilities or alternative conditional probabilities.