Which of the following statement is FALSE about the sample space of the specified experiment?

Question

A. Rolling a die once: S = {1,2,3,4,5,6}

B. Answering a True or False item: S = {True , False}

C. Tossing two fair coins once: S = {HH, HT, TH, TT}

D. Drawing a Jack from a standard deck of playing cards: S= {Jack of spades,Jack of clubs,Jack of hearts,Jack of diamonds}

Answer 1

A is True, 6 possible outcomes. Roll the die and it has to come up 1,2,3,4,5 or 6. Although it could theoretially land on its edge with no number as an outcome, or a tie between two numbers on either side of the edge. or a tie between 3 numbers as it lands on a point which connects 3 edges.

D seems to be True. 4 possible outcomes, given that you drew a Jack. But who ever devised this question might not be assuming you drew a jack then there's be 52 possible outcomes, or 54 is you include 2 wild cards, and the wild cards could be treated as jacks, making 6 possible jacks in one draw of a jack. A "stardard deck" usually includes 2 jokers. So even if only jack outcomes are considered, you have 6 possibilities, jack of spades, clubs, hearts, or diamonds, or either of the wild cards used as a jack of any of the 4 suits.

B seems to be True, as there are only two possible outcomes if you answer the question. If you left it blank on a test or answered both, then there would be 4 possible outcomes, T, F, T&F, and ~T&~F

Invoke the donkey who is equidistant to two bales of hay and can't decide which to eat, so he starves to death, but unlike the donkey which can't eat both bales, the student can choose both True and False, and hope the machine grading it will give credit.

C seems to be more True, But if order of the outcomes doesn't matter then there are just 3 possible outcomes of two coins, HH and TT as HT=TH,

If one answer is false, either D or B might be the "best" candidates for being false. An edge to D though, more likely false answer. C is least false. D more false than B, if one reallly is false.

Best answer though is all 4 are True, as the only ways to make one False is to introduce questionable other outcomes.

if the "correct" answer is more than one False answer

then

select D, then B, if 2 are wrong

select D, B and C if 3 are wrong

select all 4, if 4 are wrong.

The problem could be worded better.

if there's just one False answer and you said all 4 were correct, you'd score 75 on the question, which is a letter grade of C, and passing.

Answer 2

In answer D, the sample space is the deck of 52 playing cards {A-hearts, 2-hearts, 3-hearts, . . .}.

The successes = {Jack of spades, Jack of clubs, Jack of hearts, Jack of diamonds} not the sample space.