Practice Problems for  the Lander Math Contest
Module 12, Problems (36-38)

36)
What is the number of outcomes for the lottery 4 +1? You
pick 4 out of 56 and 1 out of 46.

37) There are 6 fair and 9 unfair (the probability of heads is
70%) coins in the box. You pick a coin from the box, toss it 5
times and get 4 heads. What is the probability unfair?

38) In previous problem find the probability that the coin was
fair.

39) Suppose your neighbor is worried that he might have a
rare disease. He decides to get tested, and suppose that the
testing methods for this disease are accurate 99 percent of
the time (regardless of whether the results come back
positive or negative). Suppose this disease is actually quite
rare, occurring randomly in the general population in only one
of every 10,000 people.
If his test results come back positive, what are his chances of
actually having the disease?

(a) .99,
(b) .90,
(c) .10, or
(d) .01?