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Determine whether the statement below is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The numbers 4, 9, and 12 are written separately on three pieces of paper. These slips of paper are then placed in a bowl. If you draw two slips from the bowl, one at a time, without replacement, then the sample space for this experiment consists of six elements. True. The sample space is S = {(4,4), (9,9), (12,12), (4,9), (4,12), (9,12)}. True. The sample space is S = {(4,9), (4,12), (9,4), (9,12), (12,4), (12,9)}. False. The sample space is S = {(4,4), (9,9), (12,12), (4,9), (4,12), (9,4), (9,12), (12,4), (12,9)}. False. The sample space is S = {4, 9, 12}. False. The sample space is S = {(4,9), (4,12), (9,12)}.

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JeanaShupp

Answer: True. The sample space is S = {(4,9), (4,12), (9,4), (9,12), (12,4), (12,9)}.

Step-by-step explanation:

  • A sample space is a set of all possible outcomes related to the event.

Given : The numbers 4, 9, and 12 are written separately on three pieces of paper.

These slips of paper are then placed in a bowl. If you draw two slips from the bowl, one at a time, WITHOUT REPLACEMENT ( i..e sample space cannot include (4,4) , (9,9) , (12, 12) in it.), then the sample space for this experiment will be : {(4,9), (4,12), (9,4), (9,12), (12,4), (12,9)} which has six elements.

Hence, the given statement is True,

∵ The sample space is S = {(4,9), (4,12), (9,4), (9,12), (12,4), (12,9)}.

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