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)?

Rationale

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 utilize the concept of conditional probability, which is represented as P(L|C). This notation signifies the probability of event L occurring given that event C has already occurred.

A (P (L|C)) CORRECT

This choice correctly represents the conditional probability we are trying to calculate, which is the chance that a root cause is due to leadership given that it's also due to communication. Knowing the definitions, we can directly apply the values from the root cause analysis to find this probability.

B (P (C or L)) YOUR ANSWER

This option represents the probability that a root cause is due to either communication (C) or leadership (L) or both. It does not focus on the relationship between the two events, which is necessary to determine the conditional probability P(L|C). Therefore, it does not answer the question posed.

C (P (C and L)) YOUR ANSWER

This choice indicates the probability that a root cause is due to both communication (C) and leadership (L) occurring simultaneously. While this is related to the question, it does not provide the conditional probability needed for P(L|C), making it irrelevant for this specific inquiry.

D (P (C|L)) YOUR ANSWER

This option represents the conditional probability of a root cause being due to communication (C) given that it is due to leadership (L). Although it is a valid conditional probability, it is not what the question is asking for, as we are interested in the probability of leadership given communication.

Conclusion

The probability of a root cause being attributed to leadership given that it is also attributed to communication is best expressed as P(L|C). This choice directly addresses the relationships and conditions described in the hospital's root cause analysis. By focusing on the correct conditional probability notation, we can derive meaningful insights into the factors contributing to root causes within the hospital setting.

P (L|C)

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