Applied Finite Mathematics by Rupinder Sekhon, UniqU, LLC - HTML preview

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Chapter 14. Probability: Homework

SAMPLE SPACES AND PROBABILITY

In problems 1 - 6, write a sample space for the given experiment.

Exercise 1.

A die is rolled.

(14.1){1,2,3,4,5,6}

Exercise 2.

A penny and a nickel are tossed.

Exercise 3.

A die is rolled, and a coin is tossed.

(14.2){1H,2H,3H,4H,5H,6H,1T,2T,3T,4T,5T,6T}

Exercise 4.

Three coins are tossed.

Exercise 5.

Two dice are rolled.

Table 14.1.
	1	2	3	4	5	6
1	(1, 1)	(1, 2)	(1, 3)	(1, 4)	(1, 5)	(1, 6)
2	(2, 1)	(2, 2)	(2, 3)	(2, 4)	(2, 5)	(2, 6)
3	(3, 1)	(3, 2)	(3, 3)	(3, 4)	(3, 5)	(3, 6)
4	(4, 1)	(4, 2)	(4, 3)	(4, 4)	(4, 5)	(4, 6)
5	(5, 1)	(5, 2)	(5, 3)	(5, 4)	(5, 5)	(5, 6)
6	(6, 1)	(6, 2)	(6, 3)	(6, 4)	(6, 5)	(6, 6)

Exercise 6.

A jar contains four marbles numbered 1, 2, 3, and 4. Two marbles are drawn.

In problems 7 - 12, a card is selected from a deck. Find the following probabilities.

Exercise 7.

(14.3)P(an ace)

(14.4)4/52

Exercise 8.

(14.5)P(a red card)

Exercise 9.

(14.6)P(a club)

(14.7)13/52

Exercise 10.

(14.8)P(a face card)

Exercise 11.

(14.9)P(a jack or spade)

(14.10)16/52

Exercise 12.

(14.11)P(a jack and a spade)

A jar contains 6 red, 7 white, and 7 blue marbles. If a marble is chosen at random, find the following probabilities.

Exercise 13.

(14.12)P(red)

(14.13)6/20

Exercise 14.

(14.14)P(white)

Exercise 15.

(14.15)P(red or blue)

(14.16)13/20

Exercise 16.

(14.17)P(red and blue)

Consider a family of three children. Find the following probabilities.

Exercise 17.

(14.18)P(two boys and a girl)

(14.19)3/8

Exercise 18.

(14.20)P(at least one boy)

Exercise 19.

(14.21)P(children of both sexes)

(14.22)6/8

Exercise 20.

(14.23)P(at most one girl)

Two dice are rolled. Find the following probabilities.

Exercise 21.

(14.24)P(the sum of the dice is 5)

(14.25)4/36

Exercise 22.

(14.26)P(the sum of the dice is 8)

Exercise 23.

(14.27)P(the sum is 3 or 6)

(14.28)7/36

Exercise 24.

(14.29)P(the sum is more than 10)

A jar contains four marbles numbered 1, 2, 3, and 4. If two marbles are drawn, find the following probabilities.

Exercise 25.

(14.30)P(the sum of the number is 5)

(14.31)4/12

Exercise 26.

(14.32)P(the sum of the numbers is odd)

Exercise 27.

(14.33)P(the sum of the numbers is 9)

Exercise 28.

(14.34)P(one of the numbers is 3)

MUTUALLY EXCLUSIVE EVENTS AND THE ADDITION RULE

Determine whether the following pair of events are mutually exclusive.

Exercise 29.

(14.35)A={A person earns more than $25,000}

(14.36)B={A person earns less than $20,000}

Yes

Exercise 30.

A card is drawn from a deck.

(14.37)C={It is a King}D={It is a heart}.

Exercise 31.

A die is rolled.

(14.38)E={An even number shows}

(14.39)F={A number greater than 3 shows}

Exercise 32.

Two dice are rolled.

(14.40)G={The sum of dice is 8}

(14.41)H={One die shows a 6}

Exercise 33.

Three coins are tossed.

(14.42)I={Two heads come up}

(14.43)J={At least one tail comes up}

Exercise 34.

A family has three children.

(14.44)K={First born is a boy}

(14.45)L={The family has children of both sexes}

Use the addition rule to find the following probabilities.

Exercise 35.

A card is drawn from a deck, and the events C and D are as follows:

(14.46)C={It is a king}

(14.47)D={It is a heart}

Find P(C or D).

(14.48)16/52

Exercise 36.

A die is rolled, and the events E and F are as follows:

(14.49)E={An even number shows}

(14.50)F={A number greater than 3 shows}

Find P(E or F).

Exercise 37.

Two dice are rolled, and the events G and H are as follows:

(14.51)G={The sum of dice is 8}

(14.52)H={Exactly one die shows a 6}

Find P(G or <

Applied Finite Mathematics by Rupinder Sekhon, UniqU, LLC - HTML preview

Chapter 14. Probability: Homework

SAMPLE SPACES AND PROBABILITY

MUTUALLY EXCLUSIVE EVENTS AND THE ADDITION RULE

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