Question

In: Statistics and Probability

Carol is running on the cross-country team, and she's really good at that too! It is...

Carol is running on the cross-country team, and she's really good at that too! It is estimated that Carol has a 60% probability of winning any race that she enters. There are five races left this year.

1.) What is the probability that Carol wins all five races?

2.) Following the same assumptions, what is the probability that Carol loses all five races?

3.) Why don't the answers to the previous two problems add up to 100%?

4.) Finally, what is the probability that Carol wins at least one race?

Expert Solution

probability of winning any race that she enters = p = 60% = 0.6

1.) What is the probability that Carol wins all five races?

P[ Carol wins all five races ] = p^5

P[ Carol wins all five races ] = 0.6^5

P[ Carol wins all five races ] = 0.07776

P[ Carol wins all five races ] = 7.776 %

2.) Following the same assumptions, what is the probability that Carol loses all five races?

P[ Carol loses all five races ] = ( 1 - p)^5

P[ Carol loses all five races ] = ( 1 - 0.6)^5

P[ Carol loses all five races ] = 0.4^5

P[ Carol loses all five races ] = 0.001024

P[ Carol loses all five races ] = 0.1024%

3.) Why don't the answers to the previous two problems add up to 100%?

because there are more cases of winning 1 , 2 or more races

4.) Finally, what is the probability that Carol wins at least one race?

P[ Carol wins at least one race ] = 1 - P[ Carol loses all five races ]

P[ Carol wins at least one race ] = 1 - 0.001024

P[ Carol wins at least one race ] = 0.998976

P[ Carol wins at least one race ] = 99.8976%

orchestra answered 1 year ago

Jen is on the college cross-country team. She is a vegan and tries to eat plenty...

Jen is on the college cross-country team. She is a vegan and tries to eat plenty of grains and fruits to get the carbohydrates needed for her high level of physical activity. She eats 3 meals a day and a snack in the evenings. A typical day for Jen would include eating whole grain toast and coffee for breakfast; a peanut butter sandwich, apple, bag of pretzels, and iced tea for lunch; spaghetti with marinara sauce, garlic bread, salad for...

Candice was a high school student on the track team and training for her upcoming cross-country...

Candice was a high school student on the track team and training for her upcoming cross-country meet. She woke up bright and early to complete a 10-mile run. Her workout ended up taking her a little longer than usual and she was sweating profusely. As Candice cooled down from her run, Candice’s Mom yelled from the kitchen, “Candice, your breakfast is ready! Come eat. You look so pale!” “Oh, really? I’m starving; maybe that’s why? What did you make?” “Your...

Because fruits and vegetables are perishable, ordering too many or too less can really hurt the...

Because fruits and vegetables are perishable, ordering too many or too less can really hurt the business with unnecessary cost (think inventory management). In your opinion would you rather order to much, or to less? Which cost do you feel is better of a business to "eat" if that situation presents itself?

Two cross-country running teams, called the Gazelles and the Cheetahs, participated in a (hypothetical) study in which 50% of the Gazelles and 65% of the Cheetahs used weight training to supplement a running workout.

Two cross-country running teams, called the Gazelles and the Cheetahs, participated in a (hypothetical) study in which 50% of the Gazelles and 65% of the Cheetahs used weight training to supplement a running workout. The remaining runners did not use weight training. At the end of the season, the mean improvement in race times (in seconds) for each team was as shown in the table below.Describe how the results recorded in the table might seem surprising or paradoxical.

From where highways404 (running north and south)and the 401(running east and west) cross in Toronto, car...

From where highways404 (running north and south)and the 401(running east and west) cross in Toronto, car A is 100km north of the 401 travelling south (towards the 401) at the constant speed of 100km/hour. Car B is 200km west of the 404 travelling east (towards the 404) at a constant speed of 100km/ hour. Assuming both cars do not stop, find the time that the cars are at theirminimum distance from each other.? What is that distance?

QUESTION 53 Exhibit 34-5 Country 1 Country 2 Good A Good B Good A Good B...

QUESTION 53 Exhibit 34-5 Country 1 Country 2 Good A Good B Good A Good B 100 0 75 0 80 10 60 30 60 20 45 60 40 30 30 90 20 40 15 120 0 50 0 150 Refer to Exhibit 34-5. The opportunity cost of one unit of good B is __________ for country 1 and __________ for country 2. 20A; 15A 1/20A; 1/15A 10A; 15A 1/2A; 1A 2A; 1/2A

a. Good X has a cross elasticity coefficient with good Y equal to 2.5 for good...

a. Good X has a cross elasticity coefficient with good Y equal to 2.5 for good Y. Is it likely that good X is peanut butter and good Y is jelly? Why or why not? b. Good Z has an income elasticity coefficient equal to 0.5. Is it likely that good Z is a new Ferrari? Explain. c. Give a definition for the Law of Increasing Costs. How does this law impact the opportunity cost of goods along a production...

Is a single, dominating, team member good or bad for the team and why. _____________________________________

Is a single, dominating, team member good or bad for the team and why. ________________________________________________________________________ ________________________________________________________________________________________________________________________________________________________________________________________________________________________ Should/should not your salary be kept a secret from other employees you work directly with? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ EXTRA CREDIT: Do you believe that any ONE of the four P-O-L-C leadership traits is any more important than the others or not, and why? ________________________________________________________________________ _________________________________________________________________________ ______________________________________________________________________ ________________________________________________________________________

What does it mean when there is too much talent on a team?

1. The formula ∆? = ???∆? is only good if ∆? is not too large. According...

1. The formula ∆? = ???∆? is only good if ∆? is not too large. According to your textbook, what is considered a “not too large ∆??” (a) ∆? ≈ 1 ?° or less (c) ∆? < 100 ?° or so (b) ∆? ≈ 10 ?° or less (d) ∆? < 200 ?° or so 2. In the formula ∆? = ???∆?, what is ?? (a) The specific heat of the substance (b) The thermal resistivity of the substance (c)...