Question

Independence and Exclusiveness are two topics which are important to probability and often confused. Discuss the difference between two events being independent and two events being mutually exclusive. Use examples to demonstrate the difference. Remember to explain as if you are talking to someone who knows nothing about the topic

Answer 1

Two events being independent means that the knowledge that one event occurred does not affect the chance of the other event occurring. Two events being mutually exclusive means that they cannot both happen at the same time.

Step-by-step explanation:

Two events being independent means that the knowledge that one event occurred does not affect the chance of the other event occurring. For example, if you roll a fair die twice, the outcome of the first roll does not change the probability of the outcome of the second roll. On the other hand, two events being mutually exclusive means that they cannot both happen at the same time. For instance, if you flip a coin and it lands on heads, it cannot also land on tails at the same time.

Answer 2

Independent means that one has no effect on the other. Exclusive means one cannot happen alongside the other. In simpler terms, independent events can be thought of as the chance it'll rain and how many people are flossing their teeth in the morning. Both happen, but neither one impacts the other.

Exclusive, on the other hand, means only one can happen. Lets say at nine in the evening your favorite show is on. However, you have an early morning and should be asleep by nine. You cannot both be asleep and watching your favorite show, and so these events are exclusive.