Question

Explain your choice of answer to below questions

A. Consider rolling a fair die once. Let A be the event of rolling an even number and B be the event of rolling a 3 or 5. Are A and B mutually exclusive? Without any calculations, what can you say about the independence/ dependence of the two events?

B. How would you explain the difference between independent and mutually exclusive events for someone who does not have much statistics background

Answer 1

A) if we roll a fair dice then sample space ={1,2,3,4,5,6}

the event A ={2,4,6}

the event B ={3,5}

yes A and B event are mutually exclusive because no one elements are common in two events

since when two events are not occur at same time is called mutually exclusive event,so mutually exclusive events said to be independent because we lknow that independent event are those event when probability of ocurring of one event is not affect the occuring of another event.so event A and B are independent.

B) a event is called mutually exclusive if there is no element are common in these event . an independent event are those event when occuring of one event is not depend upon occuring of another event.