The probability P is a real valued function whose domain is the set S and range is [0, 1], where S is the sample space.
The probability P is a real valued function whose domain is the set S and range is [0, 1], where S is the sample space.
The correct option is B False
Let us consider the example of rolling a die to understand these definitions better.
The sample space S = {1, 2, 3, 4, 5, 6}. We associate probability to an event.
We can define an event as 'An odd number turns up”. It is same as the set {1, 3, 5}. This is a subset of S. Similarly, any event will be a subset of S. When we are talking about probability, it is the probability of an event. We can say the input to the function probability is an event. That is, if we give an event, it will return the probability of that event. So, we will say the domain is the set of all events. This is nothing but the power set of sample space or the set of all subsets of sample space. (An event is a subset of sample space S).
So, the probability is a function from power set of all subsets of S.
False
Let us consider the example of rolling a die to understand these definitions better.
The sample space S = {1, 2, 3, 4, 5, 6}. We associate probability to an event.
We can define an event as 'An odd number turns up”. It is same as the set {1, 3, 5}. This is a subset of S. Similarly, any event will be a subset of S. When we are talking about probability, it is the probability of an event. We can say the input to the function probability is an event. That is, if we give an event, it will return the probability of that event. So, we will say the domain is the set of all events. This is nothing but the power set of sample space or the set of all subsets of sample space. (An event is a subset of sample space S).
So, the probability is a function from power set of all subsets of S.
