Exam 4: Basic Probability

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 a child or prefers hamburgers is ________.

The closing price of a company's stock tomorrow can be lower,higher or the same as today's closing price.Without any prior information that may affect the price of the stock tomorrow,the probability that it will close higher than today's close is 1/3.This is an example of using which of the following probability approach?

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 not a registered voter or does not prefer to get his/her current information from the Internet?

Statistical independence is when the outcome of one event affects the probability of another event.

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 3 vehicles were involved,what proportion of accidents involved alcohol?

A high school debating team of 4 is to be chosen from a class of 35.How many possible ways can the team be formed?

If two equally likely events A and B are mutually exclusive and collectively exhaustive,what is the probability that event A occurs?

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 is not from NSW and has not passed the EPT is ________.

If two events are collectively exhaustive,what is the probability that both occur at the same time?

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 or a child 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,given that alcohol was not involved,what proportion of the accidents were multiple 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,determine whether the year level of a student and whether the student lives in a residential college are statistically independent.

If either A or B must occur they are called mutually exclusive.

If P(A or B)= 1,then A and B must be collectively exhaustive.

Instruction 4-7 A lottery will have the following payoffs possible with their associated probabilities. Payoff Probability \ 200 0.0500 \ 25.00 0.0100 \ 100.00 0.0050 \ 500.00 0.0010 \ 5,000.00 0.0005 \ 10,000.00 0.0001 You buy a single ticket. -Referring to Instruction 4-7,if you have a winning ticket,the probability that you win at least $100.00 is ________.

There are only 4 empty rooms available in a residential college for eleven new students.Each room is considered unique so that it matters who is being assigned to which room.How many different ways can those 4 empty rooms be filled one student per room?

According to a survey of Australian households,the probability that the residents own 2 cars if annual household income is over $50,000 is 80%.Of the households surveyed,60% had incomes over $50,000 and 70% had 2 cars.The probability that annual household income is over $50,000 if the residents of a household own 2 cars is

The closing price of a company's stock tomorrow can be lower,higher or the same as today's closing price.Based on the closing price of the stock collected over the last month,25% of the days the closing price was higher than previous day's closing price,45% was lower than previous day's and 30% was the same as previous day's.Based on this information,the probability that tomorrow's closing price will be higher than today's is 25%.This is an example of using which of the following probability approach?

If P(A and B)= 0,then A and B must be mutually exclusive.

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,assume we know that a person has ordered a hamburger.The probability that this individual is a child is ________.