Consider a variation on the “random ice cream price” (pay what you roll) process: Two fair, six sided dice are rolled, but now the price is the smaller number followed by the larger number.

 

a. Determine the probability that you can afford the ice cream cone if you only have 25 cents.

Explain/justify your answer (here and throughout).

b. Determine the probability that the price is an odd number.

8. Consider another variation on the “random ice cream price” process: Two dice are rolled, but now these are 10-sided dice with the digits 0 – 9 on the sides. The price is back to being the larger number followed by the smaller number.

a. Determine the probability that the price is no more than 10 cents.

b. Determine the probability that the price is more than 50 cents.

 

 

9. Consider yet another variation on the “random ice cream price” process: Three fair, six sided dice are rolled, and the price is the largest number followed by the smallest number. If you are the customer and therefore prefer a smaller price, would you prefer to use two dice or three dice, or would you not have a preference? Explain your answer, but do not bother to perform any calculations.

10. Suppose that you encounter two traffic lights on your commute to school. Based on past experience, you judge that the probability is .45 that the first light will be red when you get to it, .35 that the second light will be red, and .25 that both lights will be red.

a. Produce a probability table to organize the given probabilities.

b. Determine the probability that at least one light will be red. Also name the relevant probability rule that you could use.

c. Determine the long-run percentage of days for which neither light will be red.

11. Consider that the 2012 U.S. Pet Ownership and Demographics Sourcebook reports that 36.5% of American households have a pet dog and 30.4% have a pet cat.

a. Does it follow from this information that 66.9% (the sum of 36.5% and 30.4%) of American households have a pet dog or a pet cat? Explain/justify your answer.

b. Based on the information given, what is the smallest possible value for the percentage of American households that have a pet dog or a pet cat?
in Statistics Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Best answer

7

11 12 13 14 15 16
12 22 23 24 25 26
13 23 33 34 35 36
14 24 34 44 45 46
15 25 35 45 55 56
16 26 36 46 56 66

The table shows the prices resulting from the throws of the dice.

a. There are 36 cells in the table and 18 of them are 25 or less. So the probability is 18/36=1/2.

b. 15 prices are odd: probability is 15/36=5/12.

8

0 10 20 30 40 50 60 70 80 90
10 11 21 31 41 51 61 71 81 91
20 21 22 32 42 52 62 72 82 92
30 31 32 33 43 53 63 73 83 93
40 41 42 43 44 54 64 74 84 94
50 51 52 53 54 55 65 75 85 95
60 61 62 63 64 65 66 76 86 96
70 71 72 73 74 75 76 77 87 97
80 81 82 83 84 85 86 87 88 98
90 91 92 93 94 95 96 97 98 99

a. There are only three cells ≤10, so probability=3%, 0.03 or 3/100.

b. We can see from the table that there are 27 cells containg 50 or less. That means there are 73 cells containing more than 50. Therefore the probability=73%, 0.73 or 73/100.

9. The lowest price is 11 cents. With 2 dice this result has a probability of 1/36. With 3 dice for this result you would need to throw three ones. But the probability is much lower, 1/216. Therefore, the customer would prefer to use two dice.

10. The possible outcomes for two signals are: (row is first light, column is second light):

  2=Red (0.35) 2=Green (0.65)
1=Red (0.45) 0.25 0.45*0.65=0.2925
1=Green (0.55) 0.55*0.35=0.1925 0.55*0.65=0.3575

11a) There are 3 possibilities (assume that owning more than one dog or more than one cat counts as one dog or one cat):

i) dog(s) only

ii) dog(s) and cat(s)

iii) cat(s) only

36.5% covers i) and ii); 30.4% covers ii) and iii).

So there is an overlap of the sets of cat and dog owners.

We don't know how many households own both animals, so we cannot simply add the percentages.

11b) dog+both=36.5%; cat+both=30.4%, so dog-cat=6.1%; total=dog+cat+both=66.9%-both.

6.1+2cat=66.9-2both; 2cat=60.8-2both; cat=30.4-both. So if 30.4% owned a cat and a dog, there would be no one who owned only a cat. 6.1% would own only a dog, and the total would be 36.5% owning a dog or cat or both. All those owning a cat would also own a dog. But 6.1% would own a dog but not a cat.

by Top Rated User (1.1m points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular tags

algebra problems solving equations word problems calculating percentages math problem geometry problems calculus problems math fraction problems trigonometry problems rounding numbers simplifying expressions solve for x order of operations probability algebra pre algebra problems word problem evaluate the expression slope intercept form statistics problems factoring polynomials solving inequalities 6th grade math how to find y intercept equation of a line sequences and series algebra 2 problems logarithmic equations solving systems of equations by substitution dividing fractions greatest common factor square roots geometric shapes graphing linear equations long division solving systems of equations least to greatest dividing decimals substitution method proving trigonometric identities least common multiple factoring polynomials ratio and proportion trig identity precalculus problems standard form of an equation solving equations with fractions http: mathhomeworkanswers.org ask# function of x calculus slope of a line through 2 points algebraic expressions solving equations with variables on both sides college algebra domain of a function solving systems of equations by elimination differential equation algebra word problems distributive property solving quadratic equations perimeter of a rectangle trinomial factoring factors of a number fraction word problems slope of a line limit of a function greater than or less than geometry division fractions how to find x intercept differentiation exponents 8th grade math simplifying fractions geometry 10th grade equivalent fractions inverse function area of a triangle elimination method story problems standard deviation integral ratios simplify systems of equations containing three variables width of a rectangle percentages area of a circle circumference of a circle place value solving triangles parallel lines mathematical proofs solving linear equations 5th grade math mixed numbers to improper fractions scientific notation problems quadratic functions number of sides of a polygon length of a rectangle statistics zeros of a function prime factorization percents algebra 1 evaluating functions derivative of a function equation area of a rectangle lowest common denominator solving systems of equations by graphing integers algebra 2 diameter of a circle dividing polynomials vertex of a parabola calculus problem perpendicular lines combining like terms complex numbers geometry word problems converting fractions to decimals finding the nth term range of a function 4th grade math greatest to least ordered pairs functions radius of a circle least common denominator slope unit conversion solve for y calculators solving radical equations calculate distance between two points area word problems equation of a tangent line multiplying fractions chemistry binomial expansion place values absolute value round to the nearest tenth common denominator sets set builder notation please help me to answer this step by step significant figures simplifying radicals arithmetic sequences median age problem trigonometry graphing derivatives number patterns adding fractions radicals midpoint of a line roots of polynomials product of two consecutive numbers limits decimals compound interest please help pre-algebra problems divisibility rules graphing functions subtracting fractions angles numbers discrete mathematics volume of a cylinder simultaneous equations integration probability of an event comparing decimals factor by grouping vectors percentage expanded forms rational irrational numbers improper fractions to mixed numbers algebra1 matrices logarithms how to complete the square mean statistics problem analytic geometry geometry problem rounding decimals 5th grade math problems solving equations with variables solving quadratic equations by completing the square simplifying trigonometric equation using identities
87,441 questions
99,039 answers
2,422 comments
16,939 users