Exam 4: Basic Probability

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?

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?

SCENARIO 4-3 A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger and 80 preferred chicken.55 of the children preferred hamburger. -Referring to Scenario 4-3, assume we know that a person prefers hamburger.The probability that this individual is a child is .

SCENARIO 4-7 The next state lottery will have the following payoffs possible with their associated probabilities. Pavoff Probability \ 2.00 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 Scenario 4-7, if you have a winning ticket, the probability that you win at least$100.00 is .

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 include both of the twin brothers?

According to a survey of American 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:

SCENARIO 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 Scenario 4-5, if a package is selected at random, the probability that it will be properly sealed 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 company is selected at random, what is the probability that the company is small to mid-sized and did not offer stock options to their board members?

If P (A or B) = 1.0, then A and B must be mutually exclusive.

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 probability a randomly selected patron prefers soda is .

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

An investment consultant is recommending a certain class of mutual funds to the clienteles based on its exceptionally high probability of gain.It is an unethical practice not toalso recommend a class of mutual funds with an exceptionally high probability of loss.

SCENARIO 4-7 The next state lottery will have the following payoffs possible with their associated probabilities. Pavoff Probability \ 2.00 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 Scenario 4-7, the probability that you win at least $100.00 is .

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

SCENARIO 4-3 A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger and 80 preferred chicken.55 of the children preferred hamburger. -Referring to Scenario 4-3, assume we know that a person prefers chicken.The probability that this individual is an adult is _.

SCENARIO 4-1 Mothers Against Drunk Driving is a very visible group whose focus is to educate the public about the harm caused by drunk drivers.A study was recently done that emphasized the problem we all face with drinking and driving.Four hundred accidents that occurred on a Saturday night were analyzed.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 Scenario 4-1, what proportion of accidents involved more than one vehicle?

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

SCENARIO 4-1 Mothers Against Drunk Driving is a very visible group whose focus is to educate the public about the harm caused by drunk drivers.A study was recently done that emphasized the problem we all face with drinking and driving.Four hundred accidents that occurred on a Saturday night were analyzed.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 Scenario 4-1, what proportion of accidents involved alcohol or a single vehicle? a) $25 / 400$ or $6.25 \%$ b) $50 / 400$ or $12.5 \%$ c) $195 / 400$ or $48.75 \%$ d) $245 / 400$ or $61.25 \%$

Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P (A and B) = 0.1.Then P (A or B) = .

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.