A burly biker dude slaps three strange looking dice in front of you and challeng

Question

A burly biker dude slaps three strange looking dice in front of you and challenges you to a $100 wager. The rules are simple: each player picks one die and rolls it once. The player with the higher number face up wins. You pick up the three dice and quickly realize that these are not ordinary dice. Die A has 6 faces, but only has the numbers 2,6,7, each appearing on two faces. Die B has numbers 1,5,9, each appearing on two faces. Die C has the numbers 3,4,8 each on two faces. On rolling any of these dice, each number on the die is equally likely to appear face up. He offers that you can pick your die first and he’ll pick one of the two remaining dice.

a) You like die B because it has a 9 that cannot be beat. Biker dude then picks die A. Use the four-step method to draw the decision tree of all outcomes, define the event of interest (the event that B wins over A), label the edge probabilities and compute the probability that you win.

b) You just lost $100. Biker dude offers to go “double or nothing” (if you lose you’ll owe him $200, but if you win, you owe nothing). This time you choose die A. Biker dude then chooses die C. Repeat your work from (a) for these two dice and calculate the probability that you win.

c) You lost again! Biker dude offers you another wager; this time raising the wager to $200 so you can win all your money back. Since die A beat B and die C beat A, you figure that die C cannot be beat. So you choose die C. Which die will biker dude pick this time and who will win?

Explanation / Answer

(a) The four step method is

(1) explore the problem : here the problem is to indetify all outcomes, event of interest and label all probabilites and compute the probability thaat i win.

(2) Plan : How to do it?

(3) Solving part: which we see now

(4) varify - answer is correct or not

Here in problem first i have selected Die B (1,5,9) and He picked Die A (2,6,7)

so different outcomes are (1,2),(1,6),(1,7),(5,2)(5,6),(5,7),(9,2)(9,6)(9,7) here first number belong to my dice throw and the second number is His dice throw.

event of interest are (5,2),(9,2)(9,6)(9,7)

As all outcomes have same probability = 1/9

so P( My win) = 4/9

(B) for second question again, i choose die A (2,6,7) and Biker dude choose die C(3,4,8)

so different outcomes are (2,3),(2,4),(2,8),(6,3),(6,4),(6,8),(7,3)(7,4)(7,8) here first number belong to my dice throw and the second number is His dice throw.

event of interest are (6,3),(6,4),(7,3),(7,4)

As all outcomes have same probability = 1/9

so P( My win) = 4/9 again

(c) I choose Die C now, now biker dude have 2 possibilities of die A and Die B

so lets discuss both possibilities.

it is clear that in case of Die A, if Biker dude choose Die A; P( biker dude winning) = 1- 4/9 = 5/9

Now if biker dude choose Die B let say what are the possible outcomes when i choose die C ( 3,4,7) and Biker dude Die B ( 1,5,9)

Possible outcomes (3,1),(3,5),(3,9),(4,1),(4,5),(4,9),(7,1)(7,5)(7,9)

so Favourable outcomes are  (3,1), (4,1), (7,1),(7,5)

As all outcomes have same probability = 1/9

so P( My win) = 4/9 again

so The biker dude will choose die B when i will choose die C and he will win again.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.