CHAPTER 2 CONDITIONAL PROBABILITY 2.10 Solve the network shown in Figure 2.4 usi
ID: 3195153 • Letter: C
Question
CHAPTER 2 CONDITIONAL PROBABILITY 2.10 Solve the network shown in Figure 2.4 using two of the same techniques as before. 32 1. Compute a big table. This network has five links, so the table will have 2 rows 2. The network has four paths from S to D. Call them A, B, C, and D. Solve for Prl BuCUD]. Be careful: only one pair of paths is independent all the rest are depen (since they have overlapping links). 2.11 A and B are events with Pr(AB-05, PrAB 0.3, Pr AB 0.1, and Pr AB01 a. What are Pr[A] and Pr B]? b. What are Pr[AIB], PrIA[B], PrIAIBI, and Pr[A[BI? c Calculate Pr[B A] from PriA]B using Bayes theorem. Aand Bare events with Pr[AB]=0.6, Pr[AB-0.3, PrAB|-0.1,and PrAB]=0.0 a. what are PrlA] and Pr[B]? b. what are Pr[AIB]. Pr[AIBI, PrB), and Pr[AIB ? c. Calculate Prl BIA] from PrIA I BI using Bayes theorem. Consider a roll of a four-sided die with each side equally likely. Let A = { 1.2, 31, B- and C 11,3) a. What are Pr|A]. Pr[B], and Pr[C]? b. What are PrlAIB]. PrIAIBuC], and PriAIBC]? 2.12 2.13 and Pr[BCIA]? What are PrIBIA], Pr[Bucl Consider a roll ofan ordinary six-sided die. LetAs|2,3,4,5), B=11,2, and C=12,5,6 2.14 a. What are PrA]. Pr[B], and PriC b. What are Pr[ Pr[A[Buc], and Pr[A]BC]? c. What are Pr B|A]. Pr[BuC|A], and Pr[BC A]? The Monte Hall Problem: This is a famous (or infamous!) probability paradox. In the television game show Let's Make a Deal, host Monte Hall was famous for offering contestants a deal and then trying to get them to change their minds. Consider the following: There are three doors. Behind one is a special prize (e.g., an expensive car), and behind the other two are booby prizes (on the show, often goats). The contestant picks a door, and then Monte Hall opens another door and shows that behind that door is booby prize. Monte Hall then offers to allow the contestant to switch and pick the other (unopened) door. Should the contestant switch? Does it make a difference? 2.15 2.16 Assume a card is selected from an ordinary deck with all selections equally likely. Calculate the following: a. Pr[04] c. PrQlQuKUA] d. Pr[QUKUA Q]Explanation / Answer
the contestant should switch ,you’ll win 2/3 of the time!
the only way to get it wrong by switching is to have picked the correct door in the first place. The odds of picking the correct door first are 1 in 3.
If I pick a door and hold, I have a 1/3 chance of winning.
My first guess is 1 in 3 — there are 3 random options, right?
If I rigidly stick with my first choice no matter what, I can’t improve my chances. Monty could add 50 doors, blow the other ones up, do a voodoo rain dance — it doesn’t matter. The best I can do with my original choice is 1 in 3. The other door must have the rest of the chances, or 2/3.
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