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Question : Write the sample space for the given experiment : 2151587

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Write the sample space for the given experiment.

1) A day of the week is selected at random

A) {weekend, weekday}

B) 7

C) {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

D) {1, 2, 3, 4, 5, 6, 7}

2) A box contains 10 red cards numbered 1 through 10. One card is drawn at random and its number is recorded.

A) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

B) {100}

C) {10}

D) {1, 10}

3) A box contains 13 white cards numbered 1 through 13. One card with a number greater than 6 is chosen. and its number is recorded.

A) {11}

B) {7, 8, 9, 10, 11, 12, 13}

C) {6, 7, 8, 9, 10, 11, 12, 13}

D) {1, 2, 3, . . . , 13}

4) A box contains 3 blue cards numbered 1 through 3, and 4 green cards numbered 1 through 4. A blue card is picked, followed by a green card.

A) {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)}

B) {12}

C) {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)}

D) {7}

5) A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. A blue card is picked, followed by a green card.

A) {7}

B) {12}

C) {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)}

D) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2)}

6) A coin is tossed, and then a die is rolled.

A) {(2, 6)}

B) {(h, 1), (h, 2), (h, 3), (h, 4), (h, 5), (h, 6), (t, 1), (t, 2), (t, 3), (t, 4), (t, 5), (t, 6)}

C) {(1, h), (2, h), (3, h), (4, h), (5, h), (6, h), (1, t), (2, t), (3, t), (4, t), (5, t), (6, t)}

D) {(h, t, 1, 2, 3, 4, 5, 6)}

7) Two people each have a box containing 3 slips of paper labeled rock, paper, and scissors. Each person draws one slip .

A) {(r, p), (r, s), (p, s)}

B) {(r, p), (r, s), (p, r), (p, s), (s, r), (s, p)}

C) {(3, 3)}

D) {(r, r), (r, p), (r, s), (p, r), (p, p), (p, s), (s, r), (s, p), (s, s)}

8) A card is selected at random from a deck and its suit is recorded. Then a coin is tossed.

A) {(4, 2)}

B) {(spade, head), (club, head), (heart, head), (diamond, head), (spade, tail), (club, tail), (heart, tail), (diamond, tail)}

C) {(head, spade), (head, club), (head, heart), (head, diamond), (tail, spade), (tail, club), (tail, heart), (tail, diamond)}

D) {(club, diamond, heart, spade, head, tail)}

9) For the purposes of a public opinion poll, respondents are classified as male or female and as high income, middle income, or low income.

A) {(female, high income), (female, low income), (male, high income), (male, middle income)}

B) {female, male, high income, middle income, low income}

C) {(female, high income), (female, middle income), (female, low income), (male, high income), (male, middle income), (male, low income)}

D) 6

A die is rolled twice. Write the indicated event in set notation.

10) The first roll is a 3.

A) {(3, 3)}

B) {(3, 1), (3, 3), (3, 5)}

C) {(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)}

D) {(3, 1), (3, 2), (3, 4), (3, 5), (3, 6)}

11) The second roll is a 6.

A) {(1, 6), (3, 6), (5, 6)}

B) {(1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 6)}

C) {(1, 6), (2, 6), (4, 6), (5, 6), (6, 6)}

D) {(3, 6)}

12) The first roll is a 2 and so is the second.

A) {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)}

B) (1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (6, 2)}

C) {(2, 2), (1, 2), (2, 1), (2, 5), (5, 2)}

D) {(2, 2)}

13) The sum of the rolls is 5.

A) {(1, 4), (2, 3), (3, 2), (4, 1)}

B) {(2, 3), (4, 1)}

C) {(2, 3), (3, 2)}

D) {(3, 2), (4, 1)}

14) The sum of the rolls is 8.

A) {(2, 6), (3, 5), (4, 4)}

B) {(2, 6), (3, 5), (5, 3), (6, 2)}

C) {(4, 4)}

D) {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}

15) The sum of the rolls is either 3 or 4.

A) {(2, 1), (3, 1), (2, 2)}

B) {(1, 2), (2, 2)}

C) {(1, 2), (2, 1), (1, 3), (3, 1), (2, 2)}

D) {(1, 2), (1, 3), (2, 2)}

16) The sum of the rolls is 13.

A) ∅

B) {(7, 6)}

C) {(6, 7), (7, 6)}

D) {(6, 7)}

17) The sum of the rolls is 9, and one roll is a 6.

A) ∅

B) {(6, 3)}

C) {(3, 6)}

D) {(6, 3), (3, 6)}

18) The sum of the rolls is either 7 or 5, and one roll is a 3.

A) {(3, 4), (3, 2)}

B) {(4, 3), (2, 3)}

C) {(3, 4), (4, 3)}

D) {(3, 4), (3, 2), (4, 3), (2, 3)}

19) Both rolls are even.

A) {(2, 4), (2, 6), (4, 2), (4, 6), (6, 2), (6, 4)}

B) {(2, 2), (4, 4), (6, 6)}

C) {(2, 2), (2, 4), (2, 6)}

D) {(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)}

Write the indicated event in set notation.

20) Three coins are flipped and more tails are obtained than heads.

A) {tth, tht, htt}

B) {ttt}

C) {ttt, tth}

D) {ttt, tth, tht, htt}

21) When four coins are tossed, exactly three tails are obtained.

[Hint: When four coins are tossed, the following 16 outcomes are possible:

HHHH HHHT HHTH HHTT

HTHH HTHT HTTH HTTT

THHH THHT THTH THTT

TTHH TTHT TTTH TTTT]

A) {HTTT, THTT, TTHT, TTTH}

B) {HTTT, THTT, TTHT, TTTH, TTTT}

C) {HTTT, THTT, TTTH}

D) {TTTH}

22) When four coins are tossed, the first three tosses come up the same.

[Hint: when four coins are tossed, the following 16 outcomes are possible:

HHHH HHHT HHTH HHTT

HTHH HTHT HTTH HTTT

THHH THHT THTH THTT

TTHH TTHT TTTH TTTT]

A) {HHH, TTT}

B) {HHHT, TTTH}

C) {HHHT, TTTH, HTTT, THHH}

D) {HHHH, HHHT, TTTH, TTTT}

23) When four coins are tossed, the last toss comes up heads.

[Hint: when four coins are tossed, the following 16 outcomes are possible:

HHHH HHHT HHTH HHTT

HTHH HTHT HTTH HTTT

THHH THHT THTH THTT

TTHH TTHT TTTH TTTT]

A) {HHHH, HHTH, HTHH, HTTH, THHH, THTH, TTHH, TTTH, HHHT}

B) {HHTH, HTHH, HTTH, THHH, THTH, TTHH, TTTH}

C) {HHHH, HHTH, HTHH, HTTH, THHH, THTH, TTHH, TTTH}

D) {HHHH, HHTH, HTHH, THHH, TTHH, TTTH}

24) The event that Charlie is selected as a board member when three board members are selected at random from the following group: Allison, Betty, Charlie, Dave, and Emily.

[The possible outcomes can be represented as follows.

ABC ABD ABE ACD ACE

ADE BCD BCE BDE CDE]

A) {ABC, ACD, ACE, BCD, BCE, CDE}

B) {ABC, ACD, ACE, BCD, CDE}

C) {CDE}

D) {ABC, ACD, ACE, BCD, BCE, CDE, BDE}

25) The event that Betty and Emily are selected as board members when three board members are selected at random from the following group: Allison, Betty, Charlie, Dave, and Emily.

[The possible outcomes can be represented as follows.

ABC ABD ABE ACD ACE

ADE BCD BCE BDE CDE]

A) {BE}

B) {ABE, BCE, BDE}

C) {ABE, BCE}

D) {ABC, ABD, ABE, ACE, ADE, BCD, BCE, BDE, CDE}

26) The event that fewer than two men are selected as board members when three board members are selected at random from the following group: Allison, Betty, Charlie, Dave, and Emily.

[The possible outcomes can be represented as follows.

ABC ABD ABE ACD ACE

ADE BCD BCE BDE CDE]

A) {ABC, ABD, ABE, ACE, ADE, BCE, BDE}

B) {ABC, ABD, ACE, ADE, BCE, BDE}

C) {ACD, BCD, CDE}

D) {ABC, ABD, ADE, BCE, BDE}

27) The event that Helen gets a prize in a competition in which two people are selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie.

[The possible outcomes can be represented as follows.

JG JH JM GJ GH GM

HJ HG HM MJ MG MH

Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize.]

A) {JH, GH, HJ, HG, HM}

B) {HJ, HG, HM}

C) {JH, GH, HJ, HG, HM, MH}

D) {JH, GH, HJ, JG, HG, HM, MH}

28) The event that George wins second prize in a competition in which two people are selected from four finalists to receive the first and second prizes. The prize winners are selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie.

[The possible outcomes can be represented as follows.

JG JH JM GJ GH GM

HJ HG HM MJ MG MH

Here, for example, HM represents the outcome that Helen receives the first prize and Maggie receives the second prize.]

A) {JG, HG, MG}

B) {JG, HG, MG, GM}

C) {JG, HG}

D) {JG, HG, MG, GJ, GH, GM}

29) The event that both prize winners are women in a competition in which two people are selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie.

[The possible outcomes can be represented as follows.

JG JH JM GJ GH GM

HJ HG HM MJ MG MH

Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize.]

A) {HM}

B) {HJ, HM, MH}

C) {HM, MH}

D) {HM, MH, HG, MG}

Find the probability of the given event.

30) A single fair die is rolled. The number on the die is a 3 or a 6.

A) (1/3)

B) (1/6)

C) 2

D) (1/36)

31) A single fair die is rolled. The number on the die is greater than 2.

A) (1/3)

B) (2/3)

C) (5/6)

D) (1/6)

32) A single fair die is rolled. The number on the die is not 6.

A) (5/6)

B) (1/6)

C) (35/36)

D) (2/3)

33) A single fair die is rolled. The number on the die is a multiple of 3.

A) (1/3)

B) (1/2)

C) (1/6)

D) (1/36)

34) A single fair die is rolled. The number on the die is prime.

A) (2/3)

B) 3

C) (1/3)

D) (1/2)

35) A single fair die is rolled. The number on the die is less than 6.

A) (5/7)

B) 1

C) (1/6)

D) (5/6)

36) Two fair dice are rolled. The sum of the numbers on the dice is 4.

A) (2/3)

B) 3

C) (11/12)

D) (1/12)

37) Two fair dice are rolled. The sum of the numbers on the dice is 1 or 5.

A) (1/12)

B) (1/9)

C) 0

D) (1/5)

38) Two fair dice are rolled. The sum of the numbers on the dice is 6 or 11.

A) (7/36)

B) (7/6)

C) (1/66)

D) (17/36)

39) Two fair dice are rolled. The sum of the numbers on the dice is greater than 10.

A) (1/18)

B) (5/18)

C) 3

D) (1/12)