Alice and her two sisters, Betty and Carol, are avid tennis players. Betty is the best of the three sisters, and Carol plays at the same level as Alice. Alice defeats Carol 50% of the time but only defeats Betty 40% of the time. Alice’s mother offers to give her $100 if she can win two consecutive games when playing three alternating games against her two sisters. Since the games will alternate, Alice has two possibilities for the sequence of opponents. One possibility is to play the first game against Betty, followed by a game with Carol, and then another game with Betty. We will refer to this sequence as BCB. The other possible sequence is CBC.
Calculate the probability of Alice getting the $100 reward if she chooses the sequence CBC.

Answers

Answer 1

Answer:

0.484

Step-by-step explanation:

Given that:

Alice defeats Carol 50% of the time.

This implies that, the probability of defeating Carol = 0.5

Also the probability of losing to Carol = 1 - 0.5 = 0.5

Similarly, Alice defeats Betty 40% of the time.

The probability of Alice defeating Betty = 0.4 and the  probability of losing to Betty = 1 - 0.4 = 0.6

However, in as much as Alice needs to win two consecutive games, the sequence which satisfies this condition are as follows:

Let W represent Win and L represent L.

Then the conditions are WWW, WWL and LWW

Since the outcome of each game is independent of the other games.

Then, the probability that Alice wins two games against Carol CBC is:

Pr(2W - CBC) = (0.5 × 0.4 × 0.5) + ( 0.5 × 0.4 × 0.5) + ( 0.5 × 0.4 × 0.5)

Pr(2W - CBC) = 0.1 + 0.1 + 0.1

Pr(2W - CBC) = 0.3

The probability that Alice wins two games against Betty (BCB) is:

Pr(2W - BCB) = (0.4 × 0.5 × 0.4) + (0.6 × 0.5 × 0.4) + ( 0.4 × 0.5 × 0.6)

Pr(2W - BCB) =  0.08 + 0.12 + 0.12

Pr(2W - BCB) = 0.32

However, the Probability of winning two consecutive games is the result of the addition of the probability of winning two consecutive games in the sequence CBC together with the probability of winning two consecutive games in the sequence of BCB.

i.e.

Pr(2W) = Pr(2W- CBC) + Pr(2W - BCB)

Pr(2W) = 0.3+0.32

Pr(2W) = 0.62

Finally, to calculate the probability that Alice will get $100 if she chooses the sequence CBC is:

[tex]\dfrac{Pr(2W -CBC)}{Pr(2W)}= \dfrac{0.3}{0.62}[/tex]

[tex]\mathbf{\dfrac{Pr(2W -CBC)}{Pr(2W)}= 0.484}[/tex]


Related Questions

The number 80 is decreased to 73. What is the percentage by which the number was decreased, to the nearest tenth of a percent?

Answers

Answer:

8.75 as 80-73 gives 7 and 7/80x 100= 8.73 by which is the percentage it is decreased.

pls pls pls help if ur good with angles and sides ​

Answers

Answer:

∆PQR: Equilateral Triangle

∆PRT: Scalene Triangle

∆TQS: Isosceles Triangle

∆QNP: Right Triangle

Step-by-step explanation:

∆PQR is an Equilateral Triangle because all of its angles are equal (60°).

∆PRT is a Scalene Triangle because none of its sides are equal.

The triangle above it is equilateral, and one side length is 14, meaning all of its side lengths are 14.

This makes the top of ∆PRT 14. The hypotenuse is given and it’s 18.

The last side left is clearly shorter than both, meaning none of the sides are equal.

∆TQS is an Isosceles Triangle because 2 angles are equal.

The base angles are both 76°.

∆QNP is a Right Triangle because segment QN and PR are perpendicular, creating two 90° angles on both sides.

For number 10, I suggest using a graphing calculator or desmos to graph the points. (Or you can just add the points but I suggest graphing).

From there, you can count the length of each side.

Segment DE: 9

Segment EF: 8

Segment FD: 10

This makes ∆DEF in number 10 a Scalene Triangle because none of its sides are equal.

For number 11, I also suggest graphing the points and counting the sides.

Segment DE: 7

Segment EF: 9

Segment FD: 7

This makes ∆DEF in number 11 an Isosceles Triangle because 2 of its sides are equal.

Hope this helps! :)

PLEASE HELP ME!!
It’s due in a couple of hours and I’m having hard time understanding how to do these problems. It’s 40 points, 10 for each problem.

Answers

Answer:

11. f(g(3))=5 g(f(-2))=-6

12.f(g(3))=8 g(f(-2))=3

13.f(g(3))=8 g(f(-2))=3

14.f(g(3))=0  g(f(-2))=5

Step-by-step explanation:

Harold had a summer lemonade
stand where he sold small cups for
$1.25 each and large cups for $2.50
each. He made $265. If Harold sold
88 small cups, find the number of
large cups he sold.
The basketball team scored a total

Answers

Answer:

62 large cups were sold

Step-by-step explanation:

88*1.25=110

265-110=155

155/2.50=62

Which models show the problem 4/6 : 2/6 = 2? Check all that apply :​

Answers

Answer: 1st, 2nd, and 3rd option are correct :) ✨

Step-by-step explanation:

Answer:

A, B, C

Step-by-step explanation:

faud's model racing care drives an average speed of 3 feet per second. Fuad records the distance and times in a table. At this rate, how long will it take the car to travel 21 feet?

Answers

Answer:

well 3 × 7 = 21

Step-by-step explanation:

1. 0+3=3

2. 3+3=6

3. 6+3=9

4. 9+3=12

5. 12+3=15

6. 15+3=18

7. 18+3=21

So the answer is 7

pls do this i’ll give brainliest!!

Answers

Answer:

7. move to the right by 4 units and down by 5 units

8. just rotate it to the left side (180 degrees is a flat line in the opposite direction)

9. reflection is pretty easy, just pretend you are folding your paper in half. so just redraw it on the other side in the opposite direction (fold paper sideways)

Step-by-step explanation:

I’m confused, what would the answer be? I need it ASAP please

Answers

Answer:

It is A

Step-by-step explanation:

Pls help i dont understand :( will give Brainliest + 25 Points

Answers

Answer:

A

Step-by-step explanation:

plug the points into the slope formula

slope = (y2 - y1)/(x2 - x1)  Then you get the slope of -0.5

(5 - -1))/(-6-6)

6/-12

-0.5

Plug a point in to the equation of y = -0.5x + b

-1 = -0.5(6) +b

2 = b

In the triangles shown below, AABC is similar to AXYZ. Given that ZA = 50° and
ZB = 100°, what is the measurement of ZZ? * plz help

Answers

Answer:

B. 30°

Step-by-step explanation:

Given in the question that triangle ABC  and similar to triangle XYZ where ∠A = 50° ,∠B=100° then its true to say by AA { Angle-Angle} similarity ;

if ΔABC ≅ ΔXYZ then

∠A =∠X  

∠B = ∠ Y

hence ; ∠C = ∠Z

Finding angle ∠C as ;

180°-{100+50}°

180°-150° = 30°

So angle ∠Z = 30°

Mr. Collins administered a final exam to his college chemistry class. The results are shown in the following grouped frequency polygon.

According to the data shown in the graph, which of the following statements are correct?

Answers

Answer:

Only 3 students scored between 90 and 99.

13 students earned a C

25 Students scored 70 or better on the exam.

There are 40 Students in the date.

Step-by-step explanation:

HELP PLEASE.........​

Answers

Answer:

Step-by-step explanation:

Before I can answer this, please furthermore evaluate on what the acronyms MAD and IQR stand for, and I will update my answer. Thank you!

PLEASE I WILL MARK BRAINLIEST

Answers

Answer:

16 times

Step-by-step explanation:

i could give an explanation if needed

I need some help? I don't understand math at all.

Answers

Answer:

I think its 4 but not 100% sure.

264-10=16+52

Add 10 to both sides

264=16+62

subtract 16 from both sides

248=62

Divide and i got 4.

They will have the same amount after 4 weeks. We want the $$ to be equal so we write and equation that fits the information and put them to equal each other. After that it goes into the calculator. Hope this helps!!

hi, what is 1+1 and 2+3​

Answers

Answer:

1+1 is 2 and 2+3 is 5

Step-by-step explanation:

FIRST RIGHT GETS BRAINLIEST

Answers

Answer:

0?

Step-by-step explanation:

Answer 4
Because it is going down up by 2 ( if you are looking right to left)

Find the factors of each number.
2. 20
1. 14
Identify the first five multiples for each number.
4. 3
3. 2
6. 5
5. 6
8. 7
7. 8

Answers

they are listed very weirdly so i will go according to your numbering system
2- 1, 20, 2, 10, 4, &5
1- 1, 14, 2, 7

4- 3,6,9,12,15
3- 2,4,6,8,10
6-5,10,15,20,25
5- 6,12,18,24,30
8- 7,14,21,28,35
7- 8,16,24,32,40

What is the weight in pounds of the tank, as in the above case, if the tank itself weighs 20 lbs per ft of height? A. 63,424 lbs B. 42,241 lbs C. 16,151 lbs D. 10,605 lbs.

Answers

The answer should be C I’m pretty sure maybe

Please Help Due Soon!

Answers

y = 1/3x +b

1 = 1/3(9) +b

1 = 3 +b

subtract 3 from both sides

-2 = b

y = 1/3x - 2

HELP!!! DUE IN 38 MINUTES 11:22 due at 11:59pm pst​

Answers

Answer:

(1,2)

(-1,2)

(1,-2)

(-1,-2)

The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. The paper "Left Atrial Size Increases with Body Mass Index in Children" (International Journal of Cardiology [2009]:1-7) described a study in which the left atrial size was measured for a large number of children age 5 to 15 years. Based on this data, the authors concluded that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.4 mm and a standard deviation of 4.2 mm.Approximately what proportion of healthy children has left atrial diameters less than 24 mm?Approximately what proportion of healthy children has left atrial diameters greater than 32 mm?Approximately what proportion of healthy children has left atrial diameters between 25 and 30 mm?For healthy children, what is the value for which only about 20% have a larger left atrial diameter?

Answers

Answer:

so you need the value for the 20% right ?

Step-by-step explanation:

Is 8(3x+2) and 4(6x÷4) equivalent?

Answers

Answer:

x= - 8/9

Step-by-step explanation:

Elevator 1 in a building moved from ground position to a final position of +16 feet. Elevator 2 in the same building moved from ground to a final position of –25 feet. Which statement best describes the final positions of these two elevators? (1 point) Elevator 1 is 16 feet below ground level, and elevator 2 is 25 feet above ground level. Elevator 1 is 16 feet above ground level, and elevator 2 is 25 feet below ground level. Elevator 1 is 16 feet above ground level, and Elevator 2 is 25 feet below the position of Elevator 1. Elevator 1 is 16 feet below ground level, and Elevator 2 is 25 feet above the position of Elevator 1.

Answers

Answer B

Step-by-step explanation:

Answer:

it is B

Step-by-step explanation:

i already took the test please like it and give 5 stars Thank you

7t - 4 = 10t + 14 HURRY PLEASE

Answers

Answer:

7t-4=10t+14

7t-10t=14+4

-3t=18

-3t/3=18/-3

t=-6

Answer:

Pretty sure it's t = -6

Step-by-step explanation:

7t - 4 = 10t + 14

7t -10t = 14 + 4

-3t = 18

t = -6

2. What is the rule that relates values from a set of
values to a second set of values?
A. Function
C. Relation
B. Theorem
D. None of these​

Answers

Answer:

Relation

Step-by-step explanation:

The rule that relates elements of one set to elements of another set is called "Relation". Functions are special types of Relations.

prin ce insusiri se remarca sfantul si dreptul simeon

Answers

Answer:

Nu știu scuze

Step-by-step explanation:

help me with ten please

Answers

Answer:

H

Step-by-step explanation:

Miguel gave 5 items to the clerk at the store. Before taxes were added the total was 36.00. If each item was priced the same, what is the cost of one of the items?

Answers

Answer:

$7.20

Step-by-step explanation:

$36.00 for 5 items.

Divide $36.00 by 5 to find the price of 1 item.

$36/5 = $7.20

Need help ASAP have 30 minutes

Answers

Answer:

7.25

Step-by-step explanation:

if you want to know what 1 box would be you would divide 14.50 by 2 to get 7.25 i’m sorry if i did this wrong

Can someone explain both of these ratios and answers to me?

Answers

Answer:

15 ( for Herimone) And 8 ( For Stranger Things)

Step-by-step explanation:

When Herimone uses 5 grams of Pearl Sheen she creates 30 fluid ounces of love potion. Last week she created 90 ounces which is 3 times larger than 30 ounces so you have to multiply 5 by 3 to figure out the amount of Pearl Sheen she used which is 15

For stranger things they Multiplied 3 by 2 so you have to multiply 1 by 2 to get 2. Then you have to add 6 and 2 to get 8 kids.

Hope This Helps!

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