When turning in a homework problem, always use the exercise number
indicated in bold: These will be the reference numbers I use
in reporting back you standing on the homework.
13.0: Consider the sample space of two coin flips. The
sample space has 4 points of equal likelihood: HH, HT, TH, TT.
Find three events on this sample space which are pairwise independent
but not mutually independent. Naturally, prove your answer.
13.x1: Parts (a) and (b) from Sorting Switchover Programming Problem (postscript)
13.x2: Parts (c) and (f) from Sorting Switchover
Programming Problem (postscript)
13.x3: Parts (d) and (e) from Sorting Switchover
Programming Problem (postscript)
13.x4: A 5 card hand is dealt from a standard 52 card deck. Let the
events
Q
=
"The hand contains at least one Queen"
H
=
"The hand contains at least one Heart"
Calculate P(Q), P(H), P(Q or H), P(Q and H), and P(Q | H).
Be sure to calculate the easier of P(Q or H) and P(Q and H)
first!
You should find that P(Q) does not equal P(Q | H), and so these
two events are (surprisingly) not independent. Which of the two
probabilities is bigger? Give a qualitative reason for the inequality.