Exam 4: Basic Probability

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. -Referring to Instruction 4.9,if an adult is selected at random,what is the probability that he/she is a registered voter who prefers to get his/her current information from the television?

If two events are collectively exhaustive,what is the probability that one or the other occurs?

The probability that a new advertising campaign will increase sales is estimated to be 0.80.The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. -Assuming that the two events are independent,the probability that the cost is kept within budget or the campaign will increase sales is

Instruction 4-4 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 70% said that they preferred beer. 60% of the patrons were male. 80% of the males preferred beer. -Referring to Instruction 4.4,the probability a randomly selected patron is a female is _____________ .

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. -Referring to Instruction 4.10,the two events 'preferring' beer and 'preferring' wine are statistically independent.

A debating team of four is to be chosen from a class of 35.There are two twin brothers in the class.How many possible ways can the team be formed which will include only one of the twin brothers?

Instruction 4.5 In a meat-packaging plant, Machine A accounts for 60% of the plant's output, while Machine B accounts for 40% of the plant's output. In total, 4% of the packages are improperly sealed. Also, 3% of the packages are from Machine A and are improperly sealed. -Referring to Instruction 4.5,if a package is selected at random,the probability that it will be properly sealed is _____________ .

If an event has a probability of 1,then it is a(n)_____________ .

If P(A)= 0.4 and P(B)= 0.6,then A and B must be mutually exclusive.

Instruction 4.2 An alcohol awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they went out to a pub on the weekend before the exam or spent the weekend studying, and whether they did well or poorly on the exam. The following result was obtained. Did Well on Exam Did Poorly on Exam Studying for Exam 80 20 Went to a pub 30 70 -Referring to Instruction 4.2,the events 'Did Well on Exam' and 'Studying for Exam' are

Instruction 4-4 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 70% said that they preferred beer. 60% of the patrons were male. 80% of the males preferred beer. -Referring to Instruction 4.4,the probability a randomly selected patron is a female who prefers wine is _____________ .

Instruction 4.2 An alcohol awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they went out to a pub on the weekend before the exam or spent the weekend studying, and whether they did well or poorly on the exam. The following result was obtained. Did Well on Exam Did Poorly on Exam Studying for Exam 80 20 Went to a pub 30 70 -Referring to Instruction 4.2,the events 'Did Well on Exam' and 'Did Poorly on Exam' are

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

Instruction 4.2 An alcohol awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they went out to a pub on the weekend before the exam or spent the weekend studying, and whether they did well or poorly on the exam. The following result was obtained. Did Well on Exam Did Poorly on Exam Studying for Exam 80 20 Went to a pub 30 70 -Referring to Instruction 4.2,what is the probability that a randomly selected student did well on the exam and also went to a pub on the weekend before the exam?

Twelve students in a Business Statistics class are to be formed into three teams of four.How many different ways can this be done?

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

The probability that house sales will increase in the next six 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 six months is estimated to be 0.89. - The events of 'increase in house sales' and 'no increase in house sales' in the next six months are

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: -Referring to Instruction 4.1,given alcohol was involved,what proportion of accidents involved a single vehicle?

Suppose A and B are mutually exclusive events where P(A)= 0.4 and P(B)= 0.5.Then P(A or B)= _____________ .