Quiz 5


This quiz was not good.  I strongly advise all of you to practice this sort of activity with all of the terms/concepts listed at the end of the chapter.  The results of this quiz show that many in the class still have a very imprecise understanding of these terms.

1.  Give an example of two events that are disjoint.

If we were to grade this on the exam we would check for (primarily) two things:  (a) are your events actually events and (b) are the things you describe actually disjoint?   Obviously, if (a) fails, then (b) becomes much harder to grade, although sometimes there's a glimmer.  Remember that the calling card of disjoint events is that it is impossible for both to be simultaneously true.

Example of a good answer:  "The event of winning a  race and the event of winning second place in the same race."  These are events (which are outcomes from a trial --- the "trial" here is running a race) and they can't both be true simultaneously -- you can't win both first and second place in a race.

Good answer:  "When you pick out an M&M, there is no way it can be both red and brown at the same time."   This might get marked down a wee bit because it doesn't mention explicitly what the events are. Still, it's pretty clear that the trial here is to pick an M&M and the events are "the M&M is red" and "the M&M is brown."

Some not-so-good answers:

•  "calculating traffic on a rainy day and on a non-rainy day."  The events here are, I think, "rainy day" and "non-rainy day".  These are indeed disjoint, if you define "rainy day" to be a day in which any rain at all falls.  (It is possible that a day both have rain and no  rain, so you have to be careful here.)  But involving calculating traffic makes this example confusing.  Are the events meant to be  "traffic on a rainy day" vs.  "traffic on a non-rainy day"?  

• "the  probability of thunder and lightning following rain -- car wreck and driver drunk"  Two examples, I think.  The first is a probability, not a pair of events.  As events they would be "there is thunder" and "there is lightning" or maybe "there is rain".  In any case, these are (a) not events and (b) not disjoint since lightning and rain can in fact occur together.

• "the likeliness of an earthquake occurring and the likeliness of getting an A in this class."  Again, these are not events, but "likelinesses".  But if we translate them into events:  "the event an earthquake occurs this quarter" and "the event that s/he gets an A in this class", then they are not disjoint.   It's possible to get an A even if there is an earthquake, and its possible for there to be an earthquake even if someone is given an A.

• "two notes from one flute."   Again, no events mentioned.  But let's fix this:   the trial is that a flute player randomly plays a single note.  One event is "one particular note is played" and the other is that "another particular note is played."  Since flutes can't play two notes at the same time (correct me if I'm wrong, flautists), these are indeed disjoint events.

2. Give an example of two events that are independent.

Independent events are ones for which information about one gives you no information about the other.  Put differently, the events have no affect on each other.

Good example:  "The sex of your first child and the sex of your second."  The outcome of the first birth has, at least in principle, not affecto n the second birth.  

Not so good:  
• "the event that out of a class of students the probability if you picked a student at random, he/she would be over 5'5" and the probaiblity that he/she likes to eat broccoli."   This confuses events with probabilities.  A probability is a number between 0 and 1 that represents the long-term relative frequency of an event.  But the events here are "a randomly selected person likes broccoli" and "a randomly selected person is over 5'5"."  I'd be willing to believe these were independent events, since I can't see why being taller than that height should affect your taste for broccoli.  (A nutritionist might prove me wrong, however.)

• "The chance of it raining today and the chance it will rain a year form today."  Very close, but strictly speaking these are not events. Again, I know what he/she means:  "the event that it rains today" and "the event that it rains one year from today".  But be careful!

• "squirrels eating and people tripping".  I guess these are events, but its hard to see what the trial is.  Remember, events are outcomes of a trial -- i.e. some sort of experiment or action.  I suppose if you define these carefully and say "the event that a squirrel eats something in a randomly selected minute" and "the event that a randomly chosen person trips in the same minute" it might work, but what if the person trips because the squirrel ran across their path to get food?

• "probability of having a pet and having a kid".  Hopefully, you don't "have" a pet in the same way as you have a  kid.  Again, this is about probabilities, and not events.  But let's fix this:  "a randomly selected person owns a pet" and "a randomly selected person has a kid."  Now do you think these are independent?  I don't know myself.  I would suspect that people with kids are more likely to have pets, or the other way around. I would be surprised if these were independent, but would withhold judgement until seeing some data.   So if I were grading this on an exam, I'd be left wondering whether or not this person understood what "independent" meant -- and for that reason you should explain why these are independent.

• "the probability that it will be sunny in california and raining in new york."  This one is almost correct -- just fix it so that it is about events and not probabilities.