NGPF 10.4 & 10.6 Compound and Conditional Probability Quiz

An internet web hosting company, World Wide Hosting, boasts high reliability in their advertisements. To reduce any risk of servers going down, each main server has backups so that if the main server crashes, the backup can take over without any websites going offline. The probability of any main server crashing is 10%.

World Wide Hosting wants to increase the reliability of their main server, so they add a backup server that has a probability of crashing, called the failure rate, of 12%.

Assuming the servers are completely independent, use set notation to describe the probability of both servers crashing.

• P (main crash | backup crash)

• P (main crash ∩ backup crash)

• P (main crash ⋃ backup crash)

• P (backup crash | main crash)

An internet web hosting company, World Wide Hosting, boasts high reliability in their advertisements. To reduce any risk of servers going down, each main server has backups so that if the main server crashes, the backup can take over without any websites going offline. The probability of any main server crashing is 10%.

World Wide Hosting wants to increase the reliability of their main server, so they add a backup server that has a probability of crashing, called the failure rate, of 12%.

Assuming the servers are completely independent, use set notation to describe the probability of both servers crashing.

What is the probability of a network outage on any given day?

• 0.12%

• 1.2%

• 0.012%

• 14.4%

• 12%

An internet web hosting company, World Wide Hosting, boasts high reliability in their advertisements. To reduce any risk of servers going down, each main server has backups so that if the main server crashes, the backup can take over without any websites going offline. The probability of any main server crashing is 10%.

World Wide Hosting wants to increase the reliability of their main server, so they add a backup server that has a probability of crashing, called the failure rate, of 12%.

Assuming the servers are completely independent, and knowing the probability of both servers crashing on any given day,

World Wide Hosting wants to increase the reliability even more, so they add a third backup to their main server.

The third backup has a failure rate of 15%. What is the probability of a network outage with three independent servers running?

• 0.0108%

• 1.08%

• 10.8%

• 18%

• 0.18%

An internet web hosting company, World Wide Hosting, boasts high reliability in their advertisements. To reduce any risk of servers going down, each main server has backups so that if the main server crashes, the backup can take over without any websites going offline. The probability of any main server crashing is 10%.

World Wide Hosting wants to increase the reliability of their main server, so they add a backup server that has a probability of crashing, called the failure rate, of 12%.

World Wide Hosting wants to increase their reliability even more, so they add a third backup to their main server.

The third backup has a failure rate of 15%.

After some testing, World Wide Hosting finds that their servers are not completely independent.

If a server crashes due to a power surge, all backups after the failed server have a 20% increased chance of failing.

During a storm, the main server fails due to an electrical surge.

Use the new probability of two backup servers given that an electrical surge has occurred to recalculate.

What is the new probability of a network outage if the main server fails due to an electrical surge?

• 1.12%

• 1.32%

• 1.35%

• 1.52%

• 1.67%

Use the information in the two-way table shown.

What is the expected value of the following individual?

• - 67 year old man that pays a $210 per month premium

• - Has not taken a defensive driving course

• - Does not have a car with crash avoidance features

• - Lives in Collingswood, NJ (population 14,000)?

• - Receives an average payout of $1100 if they file a claim

InsurAuto sets its premiums on an individual basis. For the person described below, calculate the premium that InsurAuto must set in order to earn an expected value of $25 per policyholder per month.

Alonso is a 22 year old male who lives in New York City (population 8.4 million). He has never taken a defensive driving course but does have a car with crash avoidance features.

What is Alonso's insurance premium?

How much does he have to pay for auto insurance?

InsurAuto sets its premiums on an individual basis. For the person described below, calculate the premium that InsurAuto must set in order to earn an expected value of $25 per policyholder per month.

Aaliyah is a 43 year old woman who lives in Kirkland, WA (population 91,951). She took a defensive driving course recently but does not own a car with crash avoidance features.

What is Aaliyah's insurance premium?

How much does she have to pay for auto insurance?

For the situation, give the correct probability notation.

The probability that a damage claim is filed and it is for fire and lightning is represented as ______

• P (D ∩ F)

• P (D ∪ F)

• P (D | F)

• P (F | D)

• P (H ∩ F)

Match each word description below with the probability notation that represents the same expression.

Use the Venn diagram shown for the scenario of the related events of having an accident and being covered by auto insurance.

• P (C’ | A)

• The probability you are covered by insurance given you have an accident

• P (A ∩ C’)

• The probability you have an accident and you are not covered by insurance

• P (C | A)

• The probability you have an accident given you are covered by insurance

• P (A | C)

• The probability you are not covered by insurance given you have an accident

Use the Venn diagram shown for the scenario of the related events of having an accident and being covered by auto insurance.

The probability you are not covered by insurance given you have an accident, as a decimal.

P (C'|A) =