Suppose there are 6 runners in the finals of a 100 m sprint, Abbie, Becca, Clarice, Danna, Emma, and Francine. Answer each of the following questions.

1. An analyst, Grace, gives Abbie a 12% chance to place first and Becca an 8% chance to place second. Assume these percentages are accurate. Can we determine the probability that Abbie will place first and Becca will place second? Why or why not?

2. Grace further informs us that the two favorites to win the race are Danna and Francine. Grace gives Danna a 48% chance to win the race and Francine a 32% chance to win. Assume these percentages are accurate. Find the probability that Danna or Francine wins the race, if possible. If not possible, explain why.

3. Suppose Abbie places first. Does this mean that Grace's probabilities were wrong? Justify your answer using terms and reasoning discussed in Chapter 5.

Bonus: Can we determine who Grace thinks is third most likely to win the race? If so, who?

Step-by-step explanation:

1. Abbie's chance to place first is 12÷100 = 0.12              

and Becca's chance to place second is 8÷100= 0.08    

We can determine the probability that Abbie will place first and Becca will place second because ., Abbie gets more chance than Becca                             (0.12 -0.08 =0.04) to get first place

2. Danna's chance to place first is P(A) = 48÷100 = 0.48  

Francine's chance to place second is P(B) = 32 ÷100 = 0.38    

The probability that Danna or Francine wins the race is

=  P(A or B) = P(A) +P(B) - P(A and B)

= 0.48 +0.32 - (0.48× 0.32)  

= 0.8 - 0.15 = 0.65      

3. Yes .,that Grace's probabilities were wrong  Because Grace only informs about the winning chance of  Abbie, Becca ,Danna,and Francine.

Grace gives 12% to Abbie and 48% to Danna ., in real Abbie won the first place ., so ., Grace's probabilities were wrong

hi there!

the answer will be d: 2

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: