There are six possible outcomes on dice i.e. 1 to 6.
Prime numbers on dice are 2,3,5 i.e. three outcomes in favour of event.
So, probability of getting a prime number on dice is 3/6 = 1/2.

If A∩B=? n set is said to be mutually exclusive not mutually exhaustive. If both sets A and B have no element in common n it is a pair of mutually exclusive sets.

Event ?A and B? contains elements which are in A as well as B. It is also called intersection of two sets.

If an event has only one sample point n it is called simple event.
e.g. All heads on tossing n coins.

An unbiased coin can have head or tail as outcome i.e. re are two possible outcomes.
So, probability of getting head on an unbiased coin is 1/2.

If A∪B=S n set is said to be mutually exhaustive. If both sets A and B have toger form sample space n it is a pair of mutually exhaustive sets.

If head come on coin n red dice can have 6 outcomes so total 1*6 = 6 outcomes. And if tail come on coin n blue dice can have 6 outcomes so total 1*6 = 6 outcomes.
So, total number of possible outcomes = 6 + 6 = 12.

There are six possible outcomes on dice i.e. 1 to 6.
Composite numbers on dice are 4,6 i.e. two outcomes in favour of event.
So, probability of getting a composite number on dice is 2/6 = 1/3.

Event ?B but not A? contains elements which are present in B but not in A.
It is represented by B-A or B∩A?.

Sure event has all outcomes in favour.
So, it is denoted by sample space S.