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 due to communication (C), we need to calculate P(L|C), which reflects the likelihood of L occurring in the context of C.
A) P (L|C)
This option is correct because it directly represents the probability we are trying to calculate: the likelihood of a root cause being attributed to leadership given that it is also attributed to communication.
B) P (C or L)
This option is incorrect as it represents the probability of either communication or leadership being a root cause, rather than the specific conditional probability of leadership given communication, which is what the question asks for.
C) P (C and L)
This option is also incorrect. It signifies the joint probability of both communication and leadership occurring simultaneously but does not provide the conditional relationship needed to answer the question.
D) P (C|L)
This choice is incorrect as well. It calculates the probability of communication being a root cause given that leadership is a root cause, which is the opposite of what is required in this scenario.
Conclusion
The correct answer is definitively P(L|C) because it accurately identifies the conditional probability required by the question. All other options fail to represent the specific relationship between leadership and communication in the context of root causes, thereby not addressing the inquiry directly.