M203E Practice Quiz 4

[1] Say you roll a fair die twice.
(a) What's the chance that the first time the die comes up 2 or more?

(b) What's the chance that the first time the die comes up 2 and the 
second time the die comes up 5?

(c) What's the chance that either the first time the die comes up 2 
or the second time the die comes up 5?

[2] A bad of marbles has 3 red marbles and 5 blue marbles.
(a) If you reach into the bag and pick a marble at random,
what's the chance it is red?

(b) If you reach into the bag twice and pick a marble each time
(without replacing the marbles you pick), what's the chance 
the marbles have different colors?

(c) If you reach into the bag and pick a marble, record the color, 
and replace it back in the bag, and then reach into the bag and pick a marble
again, what's the chance now that the marbles have different colors?

[3] A fisheries official tags and releases 100 fish into a pond. 
After a short period of time (to allow the tagged fish to mix in 
with the whole fish population in the pond), she catches a sample
of 20 fish, of which 4 are tagged. What does she estimate the 
pond's fish population to be?

[4] In February 2006 a group of eight people from Lincoln won a 
jackpot valued at 177 million dollars. In an Omaha World Herald column 
(Feb 26, 2006), Harold Andersen (whom the journalism building here at
UNL is named after) wrote: ``The Lottery Commission's intent seems pretty 
obvious: Encourage more gambling by Nebraskans, in spite of the fact that the 
law of probabilities makes it less likely that a record-breaking Powerball 
payoff will strike in Nebraska again.'' Is there such a law 
of probabilities? If you flip a fair coin three times and it comes up 
heads each time, is it more likely to come up heads or tails the
next time you flip it? Justify your answer to the second question
and then indicate whether you agree or disagree with Andersen's
assertion that a second payoff is less likely as a result of there 
having been a payoff recently.