# MCS-375 Chapter 13 Homework

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"
1. 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!
2. 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.
• 13.1:
• 13.3: