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Would you like to take the "Experiments and sample space quiz?" Experiments and sample space is a random experiment which is a process by which we try to observe something uncertain. After the experiment, the result of some random experiments is known. An outcome is understood as a result of a random experiment. The set of all possible outcomes is the sample space. So, wish you all the best with this quiz. Let's go!
Questions and Answers
1.
Which of the following is an experiment?
A.
Counting the number of marbles in a jar.
B.
Measuring the volume of the jar.
C.
Choosing a marble from the jar.
D.
Determine the weight of the jar.
Correct Answer C. Choosing a marble from the jar.
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.
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2.
Which of the following is an outcome?
A.
Rolling a die.
B.
Getting a red marble from a jar full of different coloured marbles.
C.
Flipping a coin.
D.
None of the above.
Correct Answer B. Getting a red marble from a jar full of different coloured marbles.
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.
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3.
Which of these outcomes has the highest possibilities with two dices?
A.
7
B.
11
C.
3
D.
5
Correct Answer A. 7
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.
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4.
Which of these is a possible outcome in a dice?
A.
7
B.
11
C.
12
D.
None of these
Correct Answer D. None of these
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".
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5.
Two dice are thrown and the values of both dice are added. What is the sample space S?Write the answer in the following format:S = {a, b, c, d, ...., z}
A.
S = {1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12}
B.
S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
C.
S = {1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
D.
None of these
Correct Answer B. S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
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.
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6.
Outcome is defined as the results of a single trial of the experiment.
A.
True
B.
False
Correct Answer A. True
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.
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7.
Which of these cannot be a possible outcome of two dices?
A.
2
B.
4
C.
1
D.
7
Correct Answer C. 1
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.
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8.
An experiment is defined as an outcome.
A.
True
B.
False
Correct Answer B. False
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.
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9.
A card is draw from a box containing cards numbered 2, 4, 6, 8, ...., 20 (multiples of 2). Write down the sample space S. What is the total number of possible outcomes, n(S)?
A.
20
B.
10
C.
5
D.
2
Correct Answer B. 10
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.
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10.
Two dice are thrown and the values of both dice are multiplied. What is the total number of possible outcomes n(S)?
A.
36
B.
18
C.
12
D.
6
Correct Answer B. 18
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.
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