What Is Andreas Expected Quarterly Average? Round to the Nearest Whole Percent.

Solutions: Probability

Introduction to Probability

Exercise	Trouble	Solution
i	Which of the post-obit is an experiment? Tossing a money. Rolling a unmarried 6-sided dice. Choosing a marble from a jar. All of the above.	All of the above.
ii	Which of the following is an outcome? Rolling a pair of die. Landing on red. Choosing 2 marbles from a jar. None of the to a higher place.	Landing on red.
3	Which of the following experiments does Non take equally likely outcomes? Choose a number at random from 1 to 7. Toss a money. Choose a letter at random from the give-and-take School. None of the to a higher place.	Choose a letter at random from the word SCHOOL (School has 2 O'south).
4	What is the probability of choosing a vowel from the alphabet? None of the above.
5	A number from 1 to xi is called at random. What is the probability of choosing an odd number? None of the higher up.

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Certain and Impossible Events

Exercise	Problem	Solution
1	A glass jar contains 5 crimson, 3 blue and two green jelly beans. If a jelly bean is chosen at random from the jar, and so which of the post-obit is an impossible outcome? Choosing a red jelly bean. Choosing a blue jelly bean. Choosing a yellowish jelly bean. None of the above.	Choosing a yellow jelly edible bean.
2	A spinner has 7 equal sectors numbered 1 to 7. If you lot spin the spinner, then which of the following is a certain event? Landing on a number less than vii. Landing on a number less than 8. Landing on a number greater than 1. None of the above.	Landing on a number less than 8
iii	What is the probability of choosing fourteen hearts from a standard deck of 52 playing cards? 1 0 None of the above.	0; Each suit has merely 13 cards.
four	If a number is chosen at random from the following list, then what is the probability that it is prime? 2, 3, 5, 7, 11, 13, 17, 19 1 0 None of the to a higher place.	1
5	If a single 6-sided dice is rolled, and so which of the following events is neither certain nor impossible? Rolling a number less than 7. Rolling an even number. Rolling a null. None of the in a higher place.	Rolling an fifty-fifty number.

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Sample Spaces

Exercise	Problem	Solution
1	What is the sample infinite for choosing an odd number from 1 to eleven at random? 1, 2, iii, 4, v, 6, 7, 8, 9, 10, eleven {1, 2, 3, 4, v, 6, 7, eight, 9, ten, 11} {one, 3, 5, 7, 9 11} None of the above.	{one, 3, v, 7, nine xi}
2	What is the sample space for choosing a prime less than 15 at random? {2, 3, 5, 7, 11, xiii, 15} {2, three, 5, seven, 11, thirteen} {2, 3, 5, 7, 9, eleven, 13} All of the above.	{2, 3, 5, 7, 11, 13}
3	What is the sample space for choosing 1 jelly bean at random from a jar containing five blood-red, seven blueish and ii greenish jelly beans? {5, 7, 2} {5 crimson, 7 blue, 2 green} {red, blue, green} None of the above.	{cerise, blue, green}
4	What is the sample space for choosing 1 letter of the alphabet at random from 5 vowels? {a, e, i, o, u} {five, o, w, e, l} {i, ii, 3, 4, five} None of the above.	{a, due east, i, o, u}
five	What is the sample infinite for choosing 1 alphabetic character at random from the word Divide? {d, i, v, i, d, due east} {1, ii, iii, 4, 5, 6} {d, i, five, due east} None of the above.	{d, i, five, e}

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The Complement of an Outcome

Do	Problem	Solution
i	A glass jar contains v ruby, 3 bluish and 2 green jelly beans. If a jelly bean is chosen at random from the jar, what is the probability that information technology is not blue? None of the above.	1 - = Answer:
2	A student is chosen at random from a form of 16 girls and xiv boys. What is the probability that the student chosen is non a girl? 1 None of the above.	ane - = = Respond:
iii	A number from ane to five is chosen at random. What is the probability that the number chosen is not odd? 0 None of the above.	1 - = Answer:
4	If a number is chosen at random from the following list, what is the probability that it is not prime number? 2, 3, 5, 7, 11, 13, 17, 19 1 0 None of the above.	ane - = 0 Answer: 0 (this is an impossible event)
5	If a single 6-sided die is rolled, what is the probability of rolling a number that is not eight? i 0 None of the above.	P(eight) = 0; P(not 8) = 1 - 0 = 1 Answer: ane (This is a certain upshot)

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Mutually Exclusive Events

Exercise	Problem	Solution
1	Which of the following are mutually exclusive events when a single card is chosen at random from a standard deck of 52 playing cards? Choosing a vii or Choosing a order. Choosing a 7 or Choosing a jack. Choosing a 7 or Choosing a heart. None of the to a higher place.	Choosing a seven or Choosing a jack
ii	All of the following are mutually sectional events when a single 6-sided die is rolled EXCEPT: Rolling a number less than 4 or Rolling a number greater than four. Rolling a two or Rolling an odd number. Rolling a two or Rolling an even number. None of the above.	Rolling a 2 or Rolling an fifty-fifty number.
iii	Which of the post-obit are mutually exclusive events when a 24-hour interval of the calendar week is chosen at random? Choosing a Monday or Choosing a Wednesday. Choosing a Saturday or Choosing a Sunday. Choosing a weekday or Choosing a weekend day. All of the in a higher place.	All of the above.
4	A single letter of the alphabet is chosen at random from the give-and-take Teacher. All of the following are mutually exclusive events except: Choosing a T or Choosing a consonant. Choosing a T or Choosing a vowel. Choosing an Eastward or Choosing a C. None of the to a higher place.	Choosing a T or Choosing a consonant.
five	Which of the following are mutually exclusive events when a month of the year is chosen at random? Choosing August or Choosing a summer month. Choosing September or Choosing a fall calendar month. Choosing a summer calendar month or Choosing a winter month. None of the higher up.	Choosing a summer month or Choosing a winter calendar month.

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Addition Rules for Probability

Exercise	Problem	Solution
one	A twenty-four hours of the week is chosen at random. What is the probability of choosing a Mon or Tuesday? None of the to a higher place.	+ = Reply:
2	In a pet store, in that location are 6 puppies, 9 kittens, iv gerbils, and 7 parakeets. If a pet is chosen at random, what is the probability of getting a puppy or a parakeet? None of the above.	+ = = Answer:
iii	The probability of a New York teenager owning a skateboard is 0.37, of owning a wheel is 0.81, and of owning both is 0.36. If a New York teenager is chosen at random, what is the probability that the teenager owns a skateboard or a bicycle? 1.eighteen 0.vii 0.82 None of the above.	(0.37 + 0.81) - 0.36 = 0.82 Respond: 0.82
4	A number from ane to x is chosen at random. What is the probability of choosing a 5 or an fifty-fifty number? All of the higher up.	P(5) = P(fifty-fifty) = P(five or fifty-fifty) = + = = Respond:
5	A single 6-sided die is rolled. What is the probability of rolling a number greater than 3 or an fifty-fifty number? 1 None of the above.	P(greater than 3) = P(even) = P(both) = P(greater than 3 AND even) = ( + ) - = = Answer:

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Probability of Independent Events

Exercise	Problem	Solution
i	Spin a spinner numbered one to 7, and toss a coin. What is the probability of getting an odd number on the spinner and a tail on the coin? None of the above.	· = = Answer:
2	A jar contains 6 reddish balls, 3 greenish balls, five white balls and vii xanthous balls. Two balls are chosen from the jar, with replacement. What is the probability that both balls are green? None of the above.	· = = Reply:
three	In Exercise 2, what is the probability of getting a ruby and a yellow ball? All of the to a higher place.	· = = Answer:
4	Four cards are chosen from a standard deck of 52 playing cards with replacement. What is the probability of choosing four hearts in a row? None of the above.	· · · · · · = Answer:
5	A nationwide survey showed that 65% of all children in the U.s.a. dislike eating vegetables. If 4 children are chosen at random, what is the probability that all four dislike eating vegetables? (Circular your answer to the nearest percent.) eighteen% 260% 2% None of the above.	65% = .65; (.65)(.65)(.65)(.65) = .179 .179 rounded to the nearest pct is 18% Answer: xviii%

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Probability of Dependent Events

Practice

Problem

Solution

ane

Two cards are chosen at random from a deck of 52 cards without replacement. What is the probability of getting two kings?

None of the above.

Answer:

Ii cards are called at random from a deck of 52 cards without replacement. What is the probability that the first card is a jack and the second card is a ten?

None of the above.

Answer:

On a math test, 5 out of 20 students got an A. If three students are chosen at random without replacement, what is the probability that all three got an A on the examination?

None of the in a higher place.

Answer:

Three cards are chosen at random from a deck of 52 cards without replacement. What is the probability of getting an ace, a rex and a queen in society?

None of the to a higher place.

P(ace, rex, queen)

= · ·

Answer:

A school survey found that 7 out of 30 students walk to schoolhouse. If iv students are selected at random without replacement, what is the probability that all four walk to school?

None of the above.

Answer:

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Conditional Probability

Exercise	Problem	Solution
ane	In New York Country, 48% of all teenagers ain a skateboard and 39% of all teenagers ain a skateboard and rollerblades. What is the probability that a teenager owns rollerblades given that the teenager owns a skateboard? 87% 81% 123% None of the above.	= .8125 Answer: 81% (to the nearest percent)
two	At a centre school, xviii% of all students play football and basketball game, and 32% of all students play football. What is the probability that a educatee plays basketball game given that the student plays football? 56% 178% 50% None of the in a higher place.	= .5625 Answer: 56% (to the nearest per centum)
3	In the United States, 56% of all children become an assart and 41% of all children become an allowance and do household chores. What is the probability that a child does household chores given that the child gets an assart? 137% 97% 73% None of the above.	= .7321 Answer: 73% (to the nearest percent)
iv	In Europe, 88% of all households accept a boob tube. If information technology is known that 51% of all households accept a VCR given that they also have a boob tube, so what is the probability that a household has a VCR and a television? 58% 45% 173% None of the above.	Let A denote the event "have a boob tube" and let B announce the event "accept a VCR". Answer: 45% (to the nearest pct)
five	In New England, 84% of the houses have a garage and 65% of the houses have a garage and a back k. What is the probability that a house has a backyard given that it has a garage? 77% 109% 19% None of the above.	= .7738 Respond: 77% (to the nearest percent)

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Practice Exercises

Do	Problem	Solution
ane	Which of the post-obit is an impossible event? Choosing an odd number from 1 to 10. Getting an even number after rolling a single 6-sided die. Choosing a white marble from a jar of 25 green marbles. None of the above.	Choosing a white marble from a jar of 25 green marbles.
two	Which of the following is the sample space for choosing a letter of the alphabet from the word LIBRARY? {I, A} {L, I, B, R, A, R, Y} {50, I, B, R, A, Y} None of the in a higher place.	{L, I, B, R, A, Y}
3	What is the probability that a single card chosen from a deck is not an ace? None of the to a higher place.	P(not ace) = 1 - P(ace) = one - = Answer:
4	Which of the following is a certain event? Choosing a instructor from a room full of students. Choosing an odd number from the numbers i to 10. Getting a 4 after rolling a single 6-sided die. None of the above.	The probability of a certain event is equal to one. Answer: None of the above.
5	There are 4 parents, 3 students and six teachers in a room. If a person is selected at random, what is the probability that it is a instructor or a student? None of the above.	P(teacher or student) = P(teacher) + P(student) = + = Answer:
6	In a loftier school computer class there are 15 juniors and 10 seniors. Four juniors and five seniors are boys. If a student is selected at random, then what is the probability of selecting a junior or a boy? None of the above.	P(junior or boy) = P(junior) + P(male child) - P(junior and boy) = + - = = Answer:
vii	A jar contains 5 cherry, 3 greenish, ii royal and iv yellowish marbles. A marble is called at random from the jar. After replacing it, a second marble is called. What is the probability of choosing a purple and and then a scarlet marble?	P(purple, reddish) = P(majestic) · P(cherry-red) = · = = Reply:
8	Three cards are called at random from a deck without replacement. What is the probability of choosing an eight, a seven and a six, in social club? None of the above.	P(eight, 7, half-dozen) = · · = = Answer:
ix	In a shipment of 25 DVD Players, 2 are defective. If 2 DVD Players are randomly selected and tested, what is the probability that both are defective if the outset one is non replaced later on it has been tested? None of the above.	P(defective, defective) = · = = Answer:
10	In a school, 48% of the students accept a strange language class and 19% of students accept both foreign language and technology. What is the probability that a student takes engineering science given that the students takes foreign language? (Round your answer to the nearest percent.) 67% 253% xl% None of the above.	Allow FL represent foreign language = = 0.3958333... = twoscore% rounded to the nearest pct Answer: 40%

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Challenge Exercises

Practise	Problem	Solution
1	Which of the following is the sample space when 2 coins are tossed? {H, T, H, T} {H, T} {HH, HT, TH, TT} None of the to a higher place.	{HH, HT, TH, TT}
2	At Kennedy Eye Schoolhouse, three out of five students brand honor roll. What is the probability that a student does non make accolade ringlet? 65% 40% lx% None of the above.	= .60; i - .lx = .40 Answer: 40%
3	A large basket of fruit contains 3 oranges, 2 apples and five bananas. If a slice of fruit is called at random, what is the probability of getting an orangish or a banana? None of the above.	P(orange or banana) = + = = Answer:
iv	A pair of dice is rolled. What is the probability of getting a sum of 2? None of the above.	P(1 and 1) = · = Answer:
5	In a class of xxx students, there are 17 girls and 13 boys. Five are A students, and three of these students are girls. If a educatee is chosen at random, what is the probability of choosing a girl or an A educatee? None of the to a higher place.	P(girl) + P(A) - P(girls and A) = + - = Answer:
6	In the Usa, 43% of people article of clothing a seat belt while driving. If two people are called at random, what is the probability that both of them habiliment a seat belt? 86% 18% 57% None of the above.	(.43)(.43) = .1849 Answer: eighteen% (to the nearest percent)
7	Three cards are chosen at random from a deck without replacement. What is the probability of getting a jack, a ten and a nine in order? None of the above.	P(jack, x, nine) Respond:
viii	A city survey found that 25% of teenagers have a part time chore. The same survey constitute that 40% plan to attend college. If a teenager is called at random, what is the probability that the teenager has a part time job and plans to attend college? 65% fifteen% x% None of the above.	(.25)(.40) = .x Reply: 10%
ix	In a schoolhouse, fourteen% of students take drama and computer classes, and 67% have drama grade. What is the probability that a educatee takes estimator grade given that the educatee takes drama class? 81% 21% 53% None of the above.	= .2090 Answer: 21% (to the nearest percent)
10	In a shipment of 100 televisions, six are lacking. If a person buys two televisions from that shipment, what is the probability that both are lacking? None of the higher up.	P(defective, lacking) = · = = Reply: