Question

If the occurrence of one event means that another cannot happen, then the events are
(a) Bayesian
(b) Empirical
(c) Independent
(d) Mutually exclusive

Answer 1

In order to solve this problem, we need to understand the definition of all the terms. Independent events are events which have not any kind of dependence on each other. On the other hand, mutually exclusive events are events which cannot occur at the same time.

Complete step by step answer:
We are told that if one event occurs then another cannot happen.
When the occurrence of two events are not possible simultaneously then these events are called mutually exclusive events.
Let’s first understand mutually exclusive events.
Let's understand by taking an example of a company who has a budget of 50 lacs.
And the projects available project a that is of 40 lacs and project B that is of 15 lacs.
Therefore, we cannot sign two projects at a time either one event is performed or the second.
Therefore, event A and event B are mutually exclusive events.
We can also understand it better by taking an example of rolling a die.
When a random die is thrown there is no chance that two events will occur simultaneously.
Therefore, these two events are mutually exclusive events.

So, the correct answer is “Option d”.

Note: We cannot mix mutually exclusive events with independent events. Independent events have no impact on the viability of other options. In the example of rolling a die, the event of getting a number and getting a number once again with another throw has no relation in them. Thus, these events are independent events, while the events where we get two numbers at one roll is impossible. So, these events are mutually exclusive events.