What is the sample space for a random 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 does it mean if a sample space is said to be continuous?

A continuous sample space is based on the same principles, but it has an infinite number of items in the space. In other words, you can’t write out the space in the same way that you would write out the sample space for a die roll.

How do you find the sample space of an experiment?

There isn’t a set formula for finding the sample space unless you are given (or can solve for) the probability and specific event values. You then use the formula P = Specific Event / Sample Space, plug in the P and SE values, and cross multiply to find the SS.

What is a sample space of an event?

The set of all the possible outcomes is called the sample space of the experiment and is usually denoted by S. Any subset E of the sample space S is called an event. The sample space is S = {1,2,3,4,5,6}. E = {2,4,6} is an event, which can be described in words as ”the number is even”.

Why is it important to repeat an experiment many times?

Repeating an experiment more than once helps determine if the data was a fluke, or represents the normal case. It helps guard against jumping to conclusions without enough evidence. The number of repeats depends on many factors, including the spread of the data and the availability of resources.

What is a continuous random variable?

A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile.

Can a sample space be continuous?

A sample space S is either discrete or continuous. A discrete sample space S is either finite or countably infinite. A continuous sample space S is uncountably infinite.

Which of the following refers to a sample space that is finite or countably infinite?

An event is a subspace of the sample space of a random experiment. A sample space is discrete if it consists of a finite (or countably infinite) set of outcomes.

How will you find or determine the outcome sample space using the experiment?

How do we find a sample space? To determine the sample space of an experiment, we list ALL the possible outcomes of the experiment. You may have noticed that the sample space is found by listing all the possible outcomes of the experiment.

What is the sample space formula?

Sample space refers to all possible outcomes of an experiment. So, in this case, the sample space (S) will be = (H, T). When two coins are tossed, there are four possible outcomes, i.e., S = (HH, HT, TH, TT).

What is infinite sample space?

• A chemist carries out an experiment with some chemical. mixture and observes the resulting temperature. • The sample space then consists of all possible positive. numbers, if he uses the absolute scale. This is an infinite sample space.

How do you write a sample space?

You could write the sample space another way, by just adding up the two dice. For example [1][1] = 2 and [1][2] = 3. That would give you a sample space of {2, 3, 4, 6, 7, 8, 9, 10, 11, 12}.

Were the results of the experiment the same as the predictions?

The results of the experiment were the same as the predictions made by Rutherford. What was the importance of the experimental results and the predictions being the same? (1) (Total 6 marks)

How did Rutherford predict the proportion of alpha particles?

(3) (ii) Using the nuclear model, the scientist E. Rutherford devised an equation to predict the proportion of alpha particles that would be deflected through various angles. The results of the experiment were the same as the predictions made by Rutherford.

Can we produce a controlled nuclear fusion reaction?

(1) (b) For many years, scientists have tried to produce a controlled nuclear fusion reaction that lasts long enough to be useful. However, the experimental fusion reactors use more energy than they produce.

What is the probability of students getting more than 70\% in tests?

The percentage of marks obtained by a student in the monthly tests are given below: Based on the above table, find the probability of students getting more than 70\% marks in a test. Solution: The total number of tests conducted is 5. The number of tests when students obtained more than 70\% marks = 3. So, P (scoring more than 70\% marks) = ⅗ = 0.6 4.