Sample Space of a Die and a Coin

What is Sample Space?

The sample space (S) is the set of all possible outcomes of an experiment.

What is the Sample Space for Rolling a Die and Tossing a Coin simultaneously?

The sample space for rolling a die and tossing a coin together consists of 12 outcomes: {(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}, where the first element in each pair is the die roll (1-6) and the second is the coin toss (H for heads, T for tails).

How is Sample Space determined?

The sample space is determined by listing all possible outcomes of an experiment or by using the Cartesian product of individual outcomes for each component of the experiment.

What is difference between an Event and a Sample Point?

A sample point is a single outcome of an experiment, while an event is a subset of the sample space, consisting of one or more sample points.

How is Probability Calculated from the Sample Space?

Probability (P) is calculated by dividing the number of favorable outcomes by the total number of possible outcomes: P(A) = (Number of favorable outcomes)/(Total number of possible outcomes)

Sample Space refers to the set of all possible outcomes of a random experiment or process. When a die is rolled, the total number of elements in the sample space is 6 while when a coin is tossed, there are a total of two possible outcomes.

Let’s learn how to find the Sample Space of Rolling a Die and Tossing a Coin together and separately, with the help of examples.