Exam 4: Basic Probability

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

A business venture can result in the following outcomes (with their corresponding chance of occurring in parentheses): Highly Successful (10%),Successful (25%),Break Even (25%),Disappointing (20%),and Highly Disappointing (?).If these are the only outcomes possible for the business venture,what is the chance that the business venture will be considered Highly Disappointing?

SCENARIO 4-4 Suppose that patrons of a restaurant were asked whether they preferred water or whether they preferred soda.70% said that they preferred water.60% of the patrons were male.80% of the males preferred water. -Referring to Scenario 4-4,the two events "preferring water" and "being a male" are independent.

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

SCENARIO 4-10 Are whites more likely to claim bias? It was found that 60% of the workers were white,30% were black and 10% are other races.Given that a worker was white,the probability that the worker had claimed bias was 30%.Given that a worker was black,the probability that the worker had claimed bias was 40%.Given that a worker was other race,the probability that the worker had claimed bias was 0%. -Referring to Scenario 4-10,what is the probability that a randomly selected worker had not claimed bias?

A debate team of 4 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 not include any of the twin brothers?

There are only 4 empty rooms available in a student dormitory for eleven new freshmen.All the rooms are considered as homogenous so that it does not matter who is being assigned to which room.How many different ways can those 4 empty rooms be filled one student per room?

SCENARIO 4-10 Are whites more likely to claim bias? It was found that 60% of the workers were white,30% were black and 10% are other races.Given that a worker was white,the probability that the worker had claimed bias was 30%.Given that a worker was black,the probability that the worker had claimed bias was 40%.Given that a worker was other race,the probability that the worker had claimed bias was 0%. -Referring to Scenario 4-10,what is the probability that a randomly selected worker is black and had not claimed bias?

SCENARIO 4-10 Are whites more likely to claim bias? It was found that 60% of the workers were white,30% were black and 10% are other races.Given that a worker was white,the probability that the worker had claimed bias was 30%.Given that a worker was black,the probability that the worker had claimed bias was 40%.Given that a worker was other race,the probability that the worker had claimed bias was 0%. -Referring to Scenario 4-10,when a randomly selected worker was not white,what is the probability that the worker had not claimed bias?

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

The probability that a new advertising campaign will increase sales is assessed as being 0.80.The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40.If the two events are independent,the probability that the cost is kept within budget or the campaign will increase sales is:

SCENARIO 4-2 An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying,and whether they did well or poorly on the midterm.The following result was obtained. -Referring to Scenario 4-2,what is the probability that a randomly selected student did well on the midterm and went bar hopping the weekend before the midterm?

SCENARIO 4-6 At a Texas college,60% of the students are from the southern part of the state,30% are from the northern part of the state,and the remaining 10% are from out-of-state.All students must take and pass an Entry Level Math (ELM)test.60% of the southerners have passed the ELM,70% of the northerners have passed the ELM,and 90% of the out-of-staters have passed the ELM. -Referring to Scenario 4-6,if a randomly selected student is not from southern Texas,the probability the student has not passed the ELM is _____.

SCENARIO 4-9 A survey conducted by the Segal Company of New York found that in a sample of 189 large companies,40 offered stock options to their board members as part of their non-cash compensation packages.For small- to mid-sized companies,43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. -Referring to Scenario 4-9,if a randomly selected company is a large company,what is the probability that it offered stock options to their board members?

An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women and 7 men.How many different ways can this team of 5 be formed?

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

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

A 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)on a certain date in the past. 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 3.49%?

If P (A and B)= 0,then A and B must be collectively exhaustive.

SCENARIO 4-11 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 Scenario 4-11,if an adult is selected at random,what is the probability that he/she is a registered voter or prefers to get his/her current information from radio?