What is the definition of sample space in math?

In probability theory, the sample space (also called sample description space or possibility space) of an experiment or random trial is the set of all possible outcomes or results of that experiment.

How do you define sample space?

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.

What is sample space in math examples?

Sample space is a term used in mathematics to mean all possible outcomes. For example, the sample space for rolling a normal dice is {1,2,3,4,5,6} as these are all the only outcomes we can obtain. The sample space for flipping a coin is {H, T}.

What is the definition of sample in math?

A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample. The possible values and the likelihood of each is determined by the random variable’s probability distribution.

What is sample space Class 11?

Sample space: Set of all possible outcomes of a random experiment is called sample space. It is denoted by the symbol S. Example: In Toss of a coin, Sample space is Head, Tail.

How do you write sample space?

The set whose members are all possible outcome of a random experiment is called the sample space for that experiment. For our die-rolling experiment, we can write the sample space as: S = {1, 2, 3, 4, 5, 6}.

What is the sample space of 52 cards?

The sample space of 52 cards is all 52 possible outcomes, which is {Ace of Hearts, two of hearts, three of hearts…etc}.

What is a sample space in 6th grade math?

Definition: The sample space of an experiment is the set of all possible outcomes of that experiment.

What is the sample space of tossing 2 coins?

Answer: The sample space for tossing 2 coins is { TT, TH, HT, HH } and p(exactly 1 head) is 1/2. Let’s observe the experiment of tossing 2 coins. Explanation: Head(H), Tail(T) are two possible outcomes when we toss a coin.

What is the sample space of an experiment?

The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive (i.e., they cannot occur simultaneously).

What is sample space of a coin?

A sample space is the set of all possible outcomes of a random experiment. When you toss a coin, there are only two possible outcomes-heads (h) or tails (t) so the sample space for the coin toss experiment is {h,t} .

What is then sample space of 3 coins?

The sample space of a sequence of three fair coin flips is all 23 possible sequences of outcomes: {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}.

What is the sample space of tossing 4 coins?

Expert-verified answer

Given that A coin is tossed 4 times. Sample space: {HHHH,HHHT, HHTH,HHTT,HTHH,HTHT,HTTH,HTTT,THHH,THHT,THTH,THTT,TTHH,TTHT,TTTH,TTTT}. Total possible outcomes = 16.

What is the sample space of rolling a dice?

six possible outcomes

For example, if a cubical dice is rolled there are a set of all the possible outcomes where the numbers on the die become a set. Hence, the sample space has six possible outcomes: {1, 2, 3, 4, 5, 6}.

What is the sample space of rolling 3 dice?

From the information, observe that the three dices are rolled. When three dice are rolled sample space contains 6 × 6 × 6 = 216 events in form of triplet (a, b, c), where a, b, c each can take values from 1 to 6 independently. Therefore, the number of samples is 216.

What is the total number of sample space if three dice is randomly drawn?

Just as one die has six outcomes and two dice have 6² = 36 outcomes, the probability experiment of rolling three dice has 6³ = 216 outcomes.

How many sample points are in the sample space when a pair of dice is thrown once?

Example: Throwing dice

There are 6 different sample points in the sample space.

How many elements are in the sample space of tossing three different dices?

If three dices are tossed simultaneously, the number of elements in the resulting sample space is: 6.

What is a finite sample space?

If a sample space contains a finite number of elements, then the sample space is said to be a finite sample space. The sample space for the experiment of a toss of a coin is a finite sample space. It has only two sample points.

What is sample space and random variable?

A sample space is a collection of all possible outcomes of a random experiment. A random variable is a function defined on a sample space.