Probability Models

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Probability models

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Questions 1-4

113

Question 1.

What is the sample space for the random process “toss a die”?

S = {0,1, 2, 3, 4, 5, 6}

S = {odd or even}

S = {1, 2, 3, 4, 5, 6}

Correct. While the results might be classed as odd or even, the real possible outcomes are 1 through 6. It is not possible to have 0 spots show when you toss a die.

Incorrect. While the results might be classed as odd or even, the real possible outcomes are 1 through 6. It is not possible to have 0 spots show when you toss a die.

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Question 2.

What might be a reasonable sample space for how much money is spent on a typical weekend date at your school? Note that this involves too many possible outcomes to list, so the sample space is given as an interval.

S = [10, 50]

S = [-10, 200]

S = [0, 1000]

S = [0, 25]

Correct. The sample space must include all possible outcomes. It’s possible that a date could cost no money (a free campus event, for example). Also, having relatively small upper ends precludes the possibility of nice dinners out, for example. It’s impossible for a typical date to cost negative money.

Incorrect. The sample space must include all possible outcomes. It’s possible that a date could cost no money (a free campus event, for example). Also, having relatively small upper ends precludes the possibility of nice dinners out, for example. It’s impossible for a typical date to cost negative money.

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Question 3.

If flipping a coin three times, the event “one head” consists of what outcomes?

{one head and two tails}

{HTT, THT, TTH}

3/8

{HTT}

Correct. The elementary outcomes are all possible combinations of H and T for three tosses. There are eight total possible outcomes in the sample space.

Incorrect. The elementary outcomes are all possible combinations of H and T for three tosses. There are eight total possible outcomes in the sample space.

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Question 4.

If you are tossing three dice, A = {2, 3, 4, 5, 6} is an event in that sample space.

True

False

Correct. When tossing three dice, the smallest possible result is 3 (1, 1, 1). Because 2 is not in S, this is not an event.

Incorrect. When tossing three dice, the smallest possible result is 3 (1, 1, 1). Because 2 is not inS, this is not an event.

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Questions 5-6

263

Question 5.

When drawing a card from a well-shuffled deck, all fifty-two cards are equally likely. What is the probability of drawing an ace? Enter the answer as a decimal rounded to three places.

Correct. There are four aces in a deck of fifty-two cards. 4/52 = 0.0769, which rounds to 0.077.

Incorrect. There are four aces in a deck of fifty-two cards. 4/52 = 0.0769, which rounds to 0.077.

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Question 6.

When throwing fair dice, all six faces of each die are equally likely. There are thirty-six total possible outcomes (any of the six faces of die A can be matched with any of the six faces of die B). What is the probability the sum of the pips (spots) on the two faces is at least 9

11/36 = 0.306

6/36 = 0.167

4/36 = 0.111

10/36 = 0.278

Correct. The outcomes in the event “sum of the pips is at least 9” are: 3-6, 4-5, 5-4, 6-3, 5-5, 6-4, 4-6, 5-6, 6-5, and 6-6.

Incorrect. The outcomes in the event “sum of the pips is at least 9” are: 3-6, 4-5, 5-4, 6-3, 5-5, 6-4, 4-6, 5-6, 6-5, and 6-6.

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StatTutor Lesson - Probability Models

Questions 1-4

Question 1.

Question 2.

Question 3.

Question 4.

Questions 5-6

Question 5.

Question 6.