If two events A and B are independent, thena)They can be mutually excl...
B
As the events are independent means they cannot happen jointly ,so they are not mutually exclusive
If two events A and B are independent, thena)They can be mutually excl...
Explanation:
When two events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event happening. In other words, the probability of event A occurring is not influenced by the occurrence or non-occurrence of event B, and vice versa.
Mutually Exclusive:
When two events are mutually exclusive, it means that they cannot occur at the same time. If event A happens, event B cannot happen, and vice versa. For example, if you toss a coin, the outcomes of getting a head and getting a tail are mutually exclusive.
Independence and Mutually Exclusive:
If two events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event happening. However, if events A and B are mutually exclusive, it means that they cannot occur at the same time. These two concepts are contradictory.
Example:
Let's consider an example to understand this concept better. Suppose event A represents the outcome of rolling a fair die and event B represents the outcome of flipping a fair coin. Both event A and event B are independent because rolling a die does not affect the outcome of flipping a coin, and flipping a coin does not affect the outcome of rolling a die.
Now, let's say that event A is defined as rolling an even number (2, 4, or 6) on the die, and event B is defined as flipping a head on the coin. These events are not mutually exclusive because it is possible to roll an even number on the die and also flip a head on the coin.
Conclusion:
Therefore, if two events A and B are independent, they cannot be mutually exclusive. The occurrence of one event does not affect the probability of the other event happening, so they can both happen simultaneously.
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.