STA104/MTH135: Probability

Homework #4: Conditional Probability & Independence

Due: Friday, Sep 28

Text Problems are from Sheldon Ross, A First Course in Probability (6th/5th edn).

• Problems (pp. 104ff)
  

  1

  20

  28

  41

  45

  50

  58

  66

  76

• Exercises (pp. 114/118ff)

  10

  Exercise 2 from 6th edn: If A Ì B (in words, "A is a subset of B"), express the following probabilities as simply as possible: a) P(A|B) b) P(A|Bc) c) P(B|A) d) P(B|Ac)

• Another Problem
  At the end of the old TV Quiz show Let's Make a Deal, the winner would be shown three doors (1, 2, and 3) and would be told that behind one of them, chosen at random, was a new car; the other two held a worthless prize, which we'll call a goat.

  The contestant chooses one of the three doors in any way she wishes; then the host (Monty Hall), who knows which door hides the car, opens one of the two doors not chosen by the contestant, and reveals a goat (at least one of the non-chosen doors hides a goat and, since Monty knows where the car is, he can always open a non-chosen goat door).

  Monty now offers the contestant a choice: she can stick with the door she originally chose, and win whatever is behind it; or she can trade to the still-unopened other door, and win whatever is behind it.
  A) Which should she choose, and why? Choose one:

  1. Stick with her original choice
  2. Switch to the other unopened door
  3. It doesn't matter, they both offer the same chance of a car.
  B) Give a probability sample space S suitable for this problem.

Good Luck!