Exam 4: Basic Probability

A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment). Interest Rate 7.0\% 7.5\% 8.0\% 8.5\% >8.5\% Probability 0.12 0.23 0.24 0.35 0.06 If a bank is selected at random from this distribution,what is the chance that the interest rate charged on a home loan will exceed 8.0%?

If P(A and B)= 1,then A and B must be mutually exclusive.

If two events are mutually exclusive and collectively exhaustive,what is the probability that both occur?

Instruction 4-9 A sample of 300 adults is selected.The contingency table below shows their registration status and their preferred source of information on current events. Preferred source of information Television Newspapers Radio Internet Voting registration status Registered 45 30 45 36 Not registered 35 44 45 20 -Referring to Instruction 4-9,if an adult is selected at random,what is the probability that he/she is a registered voter who does not prefer to get his/her current information from the Internet?

If two events are mutually exclusive,what is the probability that one or the other occurs?

The closing price of a company's stock tomorrow can be lower,higher or the same as today's closing price.After evaluating all the information available on the company's fundamentals and the economic environment,the probability that tomorrow's closing price will be higher than today's is determined to be 25%.This is an example of using which of the following probability approach?

Instruction 4-1 Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers.A study was recently done that emphasised the problem we all face with drinking and driving.Four hundred accidents that occurred on a Saturday night were analysed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below: Number of Vehicles involved Did alcohol play a role? Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Instruction 4-1,what proportion of accidents involved alcohol or a single vehicle?

Instruction 4-8 According to the record of the registrar's office at a university,35% of the students are first-year,25% are second-year,16% are third-year and the rest are doing their honours year.Among the first-year,second-year,third-year and honours students,the portion of students who live in a residential college are,respectively,80%,60%,30% and 20%. -Referring to Instruction 4-8,what is the probability that a randomly selected student is a first-year student who lives in a residential college?

Instruction 4-1 Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers.A study was recently done that emphasised the problem we all face with drinking and driving.Four hundred accidents that occurred on a Saturday night were analysed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below: Number of Vehicles involved Did alcohol play a role? Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Instruction 4-1,what proportion of accidents involved more than one vehicle?

Eleven students are to be assigned to eleven empty rooms in a residential college.Each room is considered unique so that it matters who is being assigned to which room.How many different ways can those eleven students be allocated?

The collection of all the possible events is called a sample space.

There are 47 contestants at a national dog show.How many different ways can contestants fill the first place,second place,and third place positions?

The probability that house sales will increase in the next 6 months is estimated to be 0.25.The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74.The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89.The probability that neither house sales nor interest rates will increase during the next 6 months is

Instruction 4-1 Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers.A study was recently done that emphasised the problem we all face with drinking and driving.Four hundred accidents that occurred on a Saturday night were analysed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below: Number of Vehicles involved Did alcohol play a role? Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Instruction 4-1,what proportion of accidents involved alcohol and a single vehicle?

If either event A or event B must occur,then events A and B are said to be

Instruction 4-3 A survey is taken among customers of fast-food restaurants to determine preference for hamburgers or chicken.Of 200 respondents selected,75 were children and 125 were adults.120 preferred hamburgers and 80 preferred chicken.55 of the children preferred hamburgers. -Referring to Instruction 4-3,the probability that a randomly selected individual is an adult and prefers chicken is ________.

If two events are independent,what is the probability that they both occur?

Instruction 4-1 Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers.A study was recently done that emphasised the problem we all face with drinking and driving.Four hundred accidents that occurred on a Saturday night were analysed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below: Number of Vehicles involved Did alcohol play a role? Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Instruction 4-1,given that alcohol was not involved,what proportion of the accidents were single vehicle?

The probability that house sales will increase in the next 6 months is estimated to be 0.25.The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74.The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89.The events of "increase in house sales" and "increase in interest rates" in the next 6 months are

Instruction 4-6 At a NSW University,60% of the students are from NSW,30% are from interstate,and the remaining 10% are from overseas.All students must take and pass an English Proficiency Test (EPT)before they graduate.60% of the NSW students have passed the EPT,70% of the interstate students have passed the EPT,and 90% of the overseas students have passed the EPT. -Referring to Instruction 4-6,the probability that a randomly selected student has passed the EPT is ________.