Sample Space of Tossing a Coin

Since a coin has two distinct sides, heads (H) and tails (T), the sample space for a single coin toss is:

S = {H,T}

Here, each element in the set represents one possible outcome when tossing the coin.

Learn, Coin Toss Probability

Sample Space of Tossing Two Coins

The sample space (S) for rolling two coins can be represented using ordered pairs, where the first element corresponds to the outcome of the first coin, and the second element corresponds to the outcome of the second coin.

Each coin has two possible outcomes.

Sample space of Tossing Two Coins is as follows:

S={(H,H),(H,T),(T,H),(T,T)}

Here, each ordered pair represents a possible combination of outcomes when rolling two coins. There are a total of 2×2=4 possible outcomes in the sample space.

Sample Space of Tossing Three Coins

The sample space (S) for rolling three coins can be represented using combinations of the possible outcomes for each coin. There are two outcomes for each coin, and there are three coins,.

Sample space of Tossing Three Coins is as follows:

S={(H,H,H),(H,H,T),(H,T,H),(T,H,H),(H,T,T),(T,H,T),(T,T,H),(T,T,T)}

Sample Space for Tossing Four Coins

The sample space (S) for rolling four coins can be represented using combinations of the possible outcomes for each coin.

Since there are two outcomes for each coin, and there are four coins, the sample space is as follows:

S = {(H,H,H,H),(H,H,H,T),(H,H,T,H),(H,T,H,H),(T,H,H,H),(H,H,T,T),(H,T,H,T),(T,H,H,T),(H,T,T,H),(T,H,T,H),(T,T,H,H),(H,T,T,T),(T,H,T,T),(T,T,H,T),(T,T,T,H),(T,T,T,T)

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.