Mutually Exclusive Events and Independent Events- myassignmenthelp

Question: Discuss about theMutually Exclusive Events and Independent Events. Answer: The statement that if two events are mutually exclusive, can be thought of as independent events, is false and I do not agree with it. This is because mutually exclusive events is a different concept from that of independent events. Events are mutually exclusive if one of the events precludes the occurrence of the other event. While in independent events the occurrence of one of the events does not affect, in anyway, the occurrence or none occurrence of the other event (Black, 2009, p. 98). This faults the notion that mutually exclusive events can be thought of as independent events. For example, mutually exclusive events can be represented as: P (A and B) = 0 While on the other hand, independent events can be represented as: P (A) P (B) = P (A and B) This shows that they are very different concepts, even in their mathematical representation. A good example, is the tossing of a coin. In this case, the expected results can either be a head or a tailthey are mutually exclusive; but not independent. This is depicted by the formula below: P (H and T) = 0 and P (H) P (T) = = 0 When two events are said to be mutually exclusive, it means that they do not occur at the same time. This means that when one occurs in a mutually exclusive situation, it excludes the chances of the other event occurring. For example, when we toss a fair coin, we can only get a head or a tailnot both. Therefore, in mutually exclusive events, only one occurrence is expected at any instance; both events cannot occur at the same time. A good example of mutually exclusive events in business is the act of a deciding to purchase something or not to purchase it. The two actions of purchasing or not purchasing are mutually exclusive events. On the other hand, independent events do not affect the occurrence of either of them. This means that, when one event occurs, it does not affect the occurrence of the other eventsneither of the events influences one another (Mukhopadhyay, 2000, p. 10). Therefore, the probability that one of the events occurs does not in any way affect the probability of the other event occurring. For example, in a business organization, the occurrence of 25 years old male employees does not affect in any way the occurrence of 25 years old female employees. References Black, K. (2009). Business Statistics: Contemporary Decision Making. John Wiley Sons. Mukhopadhyay, N. (2000). Probability and Statistical Inference. CRC Press.