Exam 4: Basic Probability

If P(A)= 0.4 and P(B)= 0.6, then A and B must be collectively exhaustive.

Suppose A and B are independent events where P(A)= 0.4 and P(B)= 0.5. Then P (A and 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, suppose a randomly selected patron prefers soda.Then the probability the patron is a male 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, assume we know the person is a child.The probability that this individual prefers hamburger is __________.

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 both house sales and interest rates will increase during the next 6 months 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 or went bar hopping the weekend before the midterm?

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

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 ethical practice to explain to the clienteles what the basis of her probability estimate is.

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

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 house sales will increase but interest rates will not during the next 6 months 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 4-11 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, is the preferred source of current information independent of the voting registration status?

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 __________.

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

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

SCENARIO 4-7 The next state lottery will have the following payoffs possible with their associated probabilities. 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 ________.

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 prefers to get his/her current information from the internet?

All the events in the sample space that are not part of the specified event are called

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 the residents of a household own 2 cars and have an income less than or equal to $50,000 a year 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 offered stock options to their board members, what is the probability that it is a large company?