a)
Check the statement; the probability of the union of two events cannot be less that the probability of their intersection is true or false.
b)
Check the statement; the probability of the union of two events cannot be more than the sum of their individual probabilities is true or false.
c)
Check the statement; the probability of intersection of two events cannot be greater than either of their individual probabilities is true or false.
d)
Check the statement; an event and its complement are mutually exclusive is true or false.
e)
Check the statement; the individual probabilities of a pair of events can not sum to more than one is true or false.
f)
Check the statement; if two events are mutually exclusive, they must also be collectively exhaustive is true or false.
g)
Check the statement; if two events are collectively exhaustive, they must also be mutually exclusive is true or false.
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Chapter 3 Solutions
Statistics for Business and Economics
- Under the investment approach, what is the likelihood that a rational voter will choose to vote and why? a. Very likely, especially if the voter derives benefit from simply expressing their opinion. b.A bout 50-50, depending on whether their candidate is ahead in the polls or not. c. Very high because they trade their vote for being able to call in a favor from the politician later. d. Almost nil because their likelihood of influencing the election is so small.arrow_forwardSuppose that there are two types of workers: high and low. Employers cannot distinguish between different types during an interview. Employers value high type at $200,000 and low type at $100,000. Employers are in a competitive market (i.e. zero profit applies). High type workers have a reservation wage of 140,000 and low type workers have a reservation wage of 80,000. Suppose that 50% of all workers are high type. The productivities, reservation wages, and the probabilities are common knowledge). What wage would the employers offer? Please explain the solution!arrow_forwardSuppose that Winnie the Pooh and Eeyore have the same value function: v(x) = x1/2 for gains and v(x) = -2(|x|)1/2 for losses. The two are also facing the same choice, between (S) $1 for sure and (G) a gamble with a 25% chance of winning $4 and a 75% chance of winning nothing. Winnie the Pooh and Eeyore both subjectively weight probabilities correctly. Winnie the Pooh codes all outcomes as gains; that is, he takes as his reference point winning nothing. For Pooh: What is the value of S? What is the value of G? Which would he choose? Eeyore codes all outcomes as losses; that is, he takes as his reference point winning $4. For Eeyore: What is the value of S? What is the value of G? Which would he choose?arrow_forward
- Assume that there are two parties, I and V. I engages in an activity that tends to injure V. V and I both can take care to reduce the expected harm from accidents. Specifically, suppose that if I takes no care (i.e., spends $0 on accident precautions), expected injury to V is $250. If I spends $40 on accident precautions, however, the expected injury to V is reduced to $175. Further suppose that V has a choice between taking no care or spending $50 in care to avoid accidents. If V spends $50 in care, V’s expected harm falls by $20 regardless of the level of care that I takes. Assume that courts adopt the socially‐optimal level of injurer care as the negligence standard. That is, if I takes less than the socially‐optimal level of care, she will be found negligent and must pay for all damages to V. If I takes at least the socially optimal level of care, she will not have to compensate V for his damages. 1. Under a negligence standard, what is I’s dominant strategy? a) I does not have a…arrow_forward2. “A risk-averse individual will always full insure, meaning that uncertainty is irrelevant.” Discuss this comment using relevant model(s) studied in the unit.arrow_forwardMicroeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)arrow_forward
- JUST ANSWER SUBPART 1 There are two individuals, Individual A and Individual B. Individual A has an income (Y) of 500 million Rupiah per year. If Individual A is sick, he will lose 25% of his income. Meanwhile, Individual B has an income (Y) of 100 million Rupiah per year, and if Individual B is sick, he will lose 75% of his income. The probability of Individual A and Individual B being sick is the same, which is 10%. If the satisfaction level of Individual A and Individual B is determined by their income level, based on the following function U(Y)=ln Y, would Individual A and Individual B prefer not to have health insurance? Explain Faced with fair actuarially insurance, how much premium is offered to Individual A? Is the premium rate offered the same for Individual B? Explain with the support of graphic illustrations. The government decides to provide compulsory health insurance with a premium rate for Individual A and Individual B, which is 2% of the income of each individual. In…arrow_forwardSuppose that an individual is just willing to accept a gamble to win or lose $1000 if the probability ofwinning is 0.6. Suppose that the utility gained if the individual wins is 100 utils. What is expected gains/loss.arrow_forwardAdam is considering what skills to study in online school. Her utility function is based on the income she earns, and is defined by U(I) = I0.8. If she learns the skill of SPSS, she will earn $145,000 per year with probability 1. If she learns the skill of Tableau, she will earn $300,000 per year with probability 0.6 (assuming that she gets the certificate) and $30,000 with probability 0.4 (if she learns without earning a certificate and she has to find a waiter job). a. Is she risk averse, risk neutral, or risk loving? Explain.b. Write out the equation for her expected utility for each skill. c.Which skill will she learn? Show your work. d.Suppose someone offers her insurance for the possibility that she does not get a Tableau certificate. This insurance will provide her an amount of income in addition to the waiter job wages that makes her indifferent between learning SPSS and Tableau. What is this amount, and what is the cost of the insurance? (note: many possible answers)arrow_forward
- Assume that there are two parties, I and V. I engages in an activity that tends to injure V. V and I both can take care to reduce the expected harm from accidents. Specifically, suppose that if I takes no care (i.e., spends $0 on accident precautions), expected injury to V is $25. If I spends $5 on accident precautions, however, the expected injury to V is reduced to $18. Further suppose that V has a choice between taking no care or spending $4 in care to avoid accidents. If V spends $4 in care, V’s expected harm falls by $2 regardless of the level of care that I takes. Assume that courts adopt the socially-optimal level of injurer care as the negligence standard. That is, if I takes less than the socially-optimal level of care, she will be found negligent and must pay for all damages to V. If I takes at least the socially optimal level of care, she will not have to compensate V for his damages. What is the Nash equilibrium of this game under a rule of no liability? Question…arrow_forwardQuestion 4 Suppose a prosecutor expects to convict a defendant with probability 0.5 and that the sentence on conviction is 10 years in prison. Assume the prosecutor values prison time at $1,000 per year (its value as a deterrent of crime), and incurs a cost of trial equal to $2,000. a. What is the minimum prison sentence the prosecutor will o er as part of a plea bargain if her objective is to maximize the expected value of the sentence imposed, less the cost of trial (ignore the information provided in b. below to answer this question a.)? b. Suppose the defendant believes his chances of being convicted are 0.3, his cost of prison time is $5,000 per year, and his cost of a trial is $1,000. Will he accept the plea bargain in a.?arrow_forwardSuppose Grace and Lisa are to go to dinner. Lisa is visiting Grace from outof town, and they are to meet at a local restaurant. When Lisa lived in town,they had two favorite restaurants: Bel Loc Diner and the Corner Stable. Ofcourse, Lisa’s information is out of date, but Grace knows which is betterthese days. Assume that the probability that the Bel Loc Diner is better isp > 1/2 and the probability that the Corner Stable is better is 1 - p. Naturedetermines which restaurant Grace thinks is better. Grace then sends amessage to Lisa, either “Let’s go to the Bel Loc Diner,” “Let’s go to theCorner Stable,” or “I don’t know [which is better].” Lisa receives the message, and then Grace and Lisa simultaneously decide which restaurant to go to. Payoffs are such that Grace and Lisa want to go to the same restaurant, but they prefer it to be the one that Grace thinks is better. More specifically, if, in fact, the Bel Loc Diner is better, then the payoffs from theiractions are as shown in the…arrow_forward