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vfiekz [6]
3 years ago
7

Last week, Robert’s family discussed insurance. He learned about some of the factors that may or may not affect each family memb

er’s need for insurance. Which situations describe something that increases the need for insurance, and which situations do not?
Increases insurance need
Does not affect insurance needs


Robert’s older brother Howard
has been working as an
electrician for the last year.
Robert’s younger sister Amelia
recently obtained her driver’s
license and has already been
at fault for a car accident.
Robert exercises regularly,
makes good grades in school,
and eats healthy food.
Robert’s uncle goes scuba
diving each summer and
enjoys snowboarding in
the winter.
Robert’s mother enjoys
scrapbooking and making
quilts in her spare time.
Robert’s grandfather, Eugene,
recently celebrated his 82nd
birthday.
​

Mathematics
1 answer:
ale4655 [162]3 years ago
5 0

Answer:

The classification are as follows;

1) Robert's older brother Howard has been working as an electrician for the last year

  • Increases insurance need

2) Robert's younger sister Amelia recently obtained her driver's licence and has already been at fault for a car accident

  • Increases insurance need

3) Robert exercises regularly makes good grades in school, and eats healthy food

  • Does not affect insurance needs

4) Robert's uncle goes scuba diving each summer and enjoys snowboarding in the winter

  • Increases insurance need

5) Robert's mother enjoys scrap-booking and making quilts in her spare time

  • Does not affect insurance needs

6) Robert's grandfather, Eugene, recently celebrated his 82nd birthday

  • Increases insurance need

Step-by-step explanation:

1) The statements are analyzed as follows;

Robert's older brother Howard has been working as an electrician for the last year

One of the four types of insurance cover that everyone needs is the long-term disability coverage, more so for Howard who is working as an electrician as 30% of new entrants into the workforce will become disabled

2) Robert's younger sister Amelia recently obtained her driver's licence and has already been at fault for a car accident

Given the likelihood of an accident occurring and the (unexpected) cost of being involved in an accident having an auto insurance will help with the expenses and protect the insurance holder against the possible litigation that results from being involved in the accident

3) Robert exercises regularly makes good grades in school, and eats healthy food

Given that Robert is a physically fit good student that eats a healthy diet, there are few potential for losses due to Robert's current status or activities, therefore, his activities does not affect insurance needs

4) Robert's uncle goes scuba diving each summer and enjoys snowboarding in the winter

Given the physical nature of Robert's uncle's activity, an accident insurance is needed which in the event of an injury, will help in taking care of the expenses so as to increase the insurance holder's peace of mind

5) Robert's mother enjoys scrap-booking and making quilts in her spare time

The activities of Robert's mother are less injury prone such that they do not affect her insurance needs

6) Robert's grandfather, Eugene, recently celebrated his 82nd birthday

Due to the age status of Robert's grandfather, it will be prudent for there to be consideration for the provision for the people that Robert's grandfather will leave behind such as mortgage payments, loans that are outstanding and possible university tuition costs that may come up in the future as well as funeral costs and daily living expenses of loved ones left behind

Therefore, there is an increased insurance need due to age status

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Answer:

0.4 = 40% probability that both marbles are blue.

0.0667 = 6.67% probability that both marbles are yellow.

53.33% probability of one blue and then one yellow

If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

Step-by-step explanation:

To solve this question, we need to understand conditional probability(for the final question) and the hypergeometric distribution(for the first three, because the balls are chosen without being replaced).

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

What is the probability that both marbles are blue?

4 + 2 = 6 total marbles, which means that N = 6

4 blue, which means that k = 4

Sample of 2, which means that n = 2

This is P(X = 2). So

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 2) = h(2,6,2,4) = \frac{C_{4,2}*C_{2,0}}{C_{6,2}} = 0.4

0.4 = 40% probability that both marbles are blue

What is the probability that both marbles are yellow?

4 + 2 = 6 total marbles, which means that N = 6

2 yellow, which means that k = 2

Sample of 2, which means that n = 2

This is P(X = 2). So

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 2) = h(2,6,2,2) = \frac{C_{2,2}*C_{4,0}}{C_{6,2}} = 0.0667

0.0667 = 6.67% probability that both marbles are yellow.

What is the probability of one blue and then one yellow?

Total is 100%.

Can be:

Both blue(40%)

Both yellow(6.67%)

One blue and one yellow(x%). So

40 + 6.67 + x = 100

x = 100 - 46.67

x = 53.33

53.33% probability of one blue and then one yellow.

If you are told that both selected marbles are the same color, what is the probability that both are blue?

Conditional probability.

Event A: Both same color

Event B: Both blue

Probability of both being same color:

Both blue(40%)

Both yellow(6.67%)

This means that P(A) = 0.4 + 0.0667 = 0.4667

Probability of both being the same color and blue:

40% probability that both are blue, which means that P(A \cap B) = 0.4

Desired probability:

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.4667} = 0.8571

If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

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Answer:

Here is the answer with the steps

Step-by-step explanation:

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3 0
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