# Probability

*label*Mathematics

*timer*Asked: Oct 22nd, 2018

*account_balance_wallet*$9.99

### Question Description

**1. There are 100 server administrators (SA) in a company. 70% are up to date with their security certification. Data shows that if an SA is up to date with certification, there is just a 5% chance that the SA will make a security error. Data also shows that if the SA is not up to date with certification, there is a 60% chance that the SA will make a security error.**

Let C stand for the event “up to date with certification” and let E stand for the event “makes a security error”.

Construct a tree diagram to answer the questions below. Use probability notation to answer the questions. For example, write “P(C ∩E) = “ or “P(C|E) = “, etc.Simplify your answers. For example: if an answer is .08/.36, then .222 is the simplified answer.

a. Insert a photo of your tree into your homework document. Place all 6 probabilities and their values on the correct branch of the tree in order to get full credit.

b. Calculate the probability that if an SA is randomly selected, you will find that the SA is up to date with certification and has not made a security error.

c. Calculate the probability that if an SA is randomly selected, you will find that the SA is not up to date with certification and has made a security error.

d. Calculate the probability that if an SA is randomly selected, you will find that the SA has made a security error. (i.e. you ae being asked to “calculate the probability of a security error.”)

e. Calculate the probability that if an SA is randomly selected from those who have made a security error, you will find that the SA is up to date with certification.

**2. A survey of 360 people who use one of three brands of probiotics is conducted in order to determine the customer satisfaction rates of the different brands. Each customer uses only one brand. The brands are: Dynamic (D), Energic (E), and Lively(L). The following tables hows the number of people who use each brand of probiotics and their satisfaction (S) with the brand they use.**

Use appropriate notation to identify the events and the probabilities requested. Do not just write a number for the answer. For example: use notation such as “P(S|D) = “. . Simplify your answer. For example: if an answer is 80/360, then .222 is the simplified answer.

State | Satisfied | Not Satisfied | Total |

Dynamic | 60 | 80 | 140 |

Energy | 60 | 20 | 80 |

Lively | 40 | 100 | 140 |

Total | 160 | 200 | 360 |

- Calculate the probability of selecting a customer whose brand is Dynamic and who is satisfied.
- Calculate the probability that an Energy customer is satisfied
- Calculate the probability that a customer who is satisfied uses the brand Dynamic or the brand Energy.
- Calculate the probability that a customer who is not satisfied uses the brand Lively.
- Using the data in the table and the formula in your textbook for independence of events, determine whether the two following two events are independent: being satisfied; using the Dynamic brand.

**3.** **In this card game, a player is dealt 10 cards. A player wins $1,000,000 if he is dealt 8 hearts. Use combinatorics to set up your problem**

- Calculate the probability a player is dealt exactly 8 hearts
- Calculate the probability a player is dealt exactly 8 hearts if the first two cards he was dealt were diamonds.

**4. Forty percent of world class tennis player are over 6 feet tall. 20 percent of the world class tennis players over 6 feet tall were premature babies. 30 percent of the world class tennis players who are not over 6 feet tall were premature babies.**

a. Calculate the probability that a randomly selected world class tennis player is over 6 feet tall and was a premature baby. Don’t just write a number for the answer. Use the probability notation, simplify the answer, and show your work.

b. Calculate the probability that a randomly selected world class tennis player is not over 6 feet tall and was not a premature baby. Don’t just write a number for the answer. Use the probability notation, simplify the answer, and show your work.

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