Compound and Conditional Probability

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?

• 12%

• 32%

• 35%

• 52%

• 67%

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 (A | C)

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

• P (C | A)

• The probability you are not 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

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 have an accident given you are covered by insurance, as a decimal to the nearest thousandth P (A | C) ≈

(a)  

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 covered by insurance given you have an accident, as a decimal P (C | A) =

(a)  

For the following situation, give the correct probability notation using the table shown.

The probability that a property damage claim is filed given a claim is filed is represented as (a)  

What is the probability that a damage claim was filed given that a damage claim was filed for wind and hail?

Mathematical Equivalence

ON

What did Toby do wrong in his calculations?

• Toby used [P(H) ⋅ cost] instead of [P(H | D) ⋅ cost]

• Toby used [P(H | D) ⋅ cost] instead of [P(H) ⋅ cost]

• Toby used [P(D | H) ⋅ cost] instead of [P(H) ⋅ cost]

• Toby used [P(H) ⋅ cost] instead of [P(D | H) ⋅ cost]

• Toby used [P(H ⋂ D) ⋅ cost] instead of [P(H) ⋅ cost]

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%

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

(a)