Experiments And Sample Space Quiz

Explanation
Choosing a marble from the jar is an experiment because it involves taking an action to observe a specific outcome. In this case, the action is selecting a marble from the jar, and the outcome is the specific marble that is chosen. The other options listed are not experiments as they do not involve actively manipulating or observing a specific outcome. Counting the number of marbles, measuring the volume of the jar, and determining the weight of the jar are all observational activities rather than experiments.

Explanation
The correct answer is "Getting a red marble from a jar full of different coloured marbles." This is an outcome because it represents a specific result or event that can occur when selecting a marble from the jar. It is a distinct possibility among the given options and can be considered as a potential outcome of the action.

Explanation
When rolling two dice, the highest possible outcome is 12 (6 on each die). However, the question asks for the outcome with the highest possibilities, meaning the outcome that can be achieved in the most ways. The only way to get a sum of 7 with two dice is by rolling a 1 and a 6, a 2 and a 5, a 3 and a 4, a 4 and a 3, a 5 and a 2, or a 6 and a 1. Therefore, 7 has the highest possibilities among the given options.

Explanation
A standard dice has six sides numbered from 1 to 6. Therefore, the possible outcomes in a dice are limited to these numbers only. The options provided in the question, 7, 11, and 12, are not possible outcomes in a dice. Thus, the correct answer is "None of these".

Explanation
The correct answer is S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. When two dice are thrown, the possible values that can be obtained by adding the values on both dice range from 2 to 12. Therefore, the sample space S consists of all these possible sums, which are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

Explanation
The outcome of an experiment refers to the specific result or results that occur after a single trial. It could be a specific measurement, observation, or event that happens as a result of conducting the experiment. Therefore, the statement that "outcome is defined as the results of a single trial of the experiment" is true.

Explanation
The question asks for a possible outcome of two dice rolls. Since each die has numbers ranging from 1 to 6, the sum of two dice rolls can range from 2 to 12. Therefore, 7 cannot be a possible outcome of two dice rolls.

Explanation
An experiment is not defined as an outcome. An experiment refers to a scientific procedure conducted to test a hypothesis or gather data, while an outcome is the result or conclusion of the experiment. Therefore, the statement is false.

Explanation
The sample space, S, represents all the possible outcomes of drawing a card from the box. In this case, the numbers on the cards are multiples of 2, ranging from 2 to 20. Therefore, the sample space S would be {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}. The total number of possible outcomes, n(S), is the count of elements in the sample space, which is 10.

Explanation
When two dice are thrown, each die can have 6 possible outcomes. Therefore, the total number of possible outcomes for both dice is 6 x 6 = 36. However, we are asked to find the total number of possible outcomes when the values of both dice are multiplied. If we consider all the possible combinations of the values of both dice, we can see that there are only 18 unique outcomes. For example, if one die shows a 1 and the other die shows a 6, the product is 1 x 6 = 6. Since there are 18 unique outcomes, the total number of possible outcomes is 18.