The expected value of spinner a is $400/100=$4; Dave should expect to get about as much as he pays in per spin with spinner a. Another way to calculate this expected value is to use the probabilities, and multiply: $5*(1/4)+$4*(1/2)+$3*(1/4) = $4

If he used spinner b, Dave would get $0 about 20 times, $5 about 40 times, $2 about 20 times and $6 about 20 times, so he would get about: 0*20+5*40+2*20+6*20=$360, so after paying $400, he would probably lose about $40.

The expected value of spinner b is $360/100=$3.60; Dave should expect to lose about $4-$3.60=$.40 per spin with spinner b. Another way to calculate this expected value is to use the probabilities, and multiply: $0*(1/5)+$5*(2/5)+$2*(1/5)+$6*(1/5) = $3.60

If he used spinner c, Dave would get $6 about 50 times, $2 about 25 times and $3 about 25 times, so he would get about 6*50+2*25+3*25=$425, so after paying $400, he would probably win about $25.

The expected value of spinner c is $425/100=$4.25; Dave should expect to win about $4.25-$4.00=$.25 per spin with spinner c. Another way to calculate this expected value is to use the probabilities, and multiply: $6*(1/2)+$2*(1/4)+$3*(1/4) = $4.25

If Dave were playing 100 times, it would be smartest to play game c.

2. If you were only going to spin once, (and it didn't matter too much if you lost all of your money, and it didn't matter how much you won or lost), b would be the best choice. However, if you are going to play several times (like Dave), you should definitely not choose b because you lose a lot when you lose, so that overall you will lose money.

3. A. Some coincidences I think are probably not genetically based are:

• their names (they didn't name themselves)
• their wives names (you don't generally choose who to date based on their name, and after all, they didn't name their wives--their wives parents did)
• the white bench around the tree (I could be wrong, but that seems like a really common thing for that decade and area of the country.)

Some coincidences that could plausibly be genetically influenced:

• that they were divorced and remarried (that sounds like a personality trait)
• that they both smoked, and perhaps the brand of cigarettes ( a tendency to smoke or drink seems to have some genetic basis, and what things taste pleasant could easily be genetically based)
• that they both drank beer, and perhaps the brand of beer (see previous)
• maybe that they disliked baseball (that could be because they weren't very good at it as a child, which could have a physical, genetic reason)
• maybe that they both stayed in Ohio (staying where you were raised seems like a personality trait)

Some coincidences that I'm not sure about

• Chevrolets--you can say its a personality trait to like driving the same kind of car, but chevrolets were everywhere in the 70's, so it's not a coincidence that stands out
• the names of the children and the dog: names tend to be very culturally based rather than genetically based, and the names are all pretty common. The Jim's did have some say over what names to give their children and dogs (they didn't name themselves or their wives), so it's not impossible that personality had something to do with it.
• their vacation spot--an awful lot of people in the midwest vacation in Florida, so that's not a big coincidence, and picking the same beach seems like an event that genetics wouldn't have much influence over.

B. If you take any two people of similar backgrounds, you are likely to find some coincidences (things they have in common). If you went out looking for one specific coincidence (like: do you have the same middle name), it would be very unlikely that it would be true about any particular pair of people you asked, but if you look at all of the hundreds of things that could be coincidences between a pair of people, you shouldn't be too surprised if some of them are true.

I did some reading after class about identical twins, and there seem to be a lot of coincidences that people find, and that seem to be genetic, but it seems to be really hard to measure, and they things that are the same across twins that are raised in different backgrounds (as opposed to being raised in two different families, but both in the same state, and same socio economic status, etc.) are pretty subtle.