Consider the following. (Assume that the dice are distinguishable and that what is observed are the numbers that face up.) HINT [See Examples 1-3.] Two distinguishable dice are rolled; the numbers add to 7. Describe the sample space S of the experiment. (Select all that apply.)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (2,7) (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) (6,7) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (5,7) (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
List the elements of the given event. (Select all that apply.)
(6,1) (5,2) (4,3) (3,4) (2,5) (1,6) (6,4) (5,5) (4,6) (1,2) (2,1) (6,1) (5,2) (4,3) (6,3) (5,4) (4,5) (3,6) (6,6) (1,1) (3,1) (2,2) (1,3) (5,6) (6,5)
Consider the following. (Assume that the dice are distinguishable and that what is observed are t...
Calculate the probability of the following events: C = the sum of the digits is less than or equal to 6 D = the sum of the digits is greater than or equal to 7 P(C) P(D) P(C or D) P(C and D) 2 Dice Sample Space 1,11,21,31,41,51,62,12,22,32,42,52,63,13,23,33,43,53,64,14,24,34,44,54,65,15,25,35,45,55,66,16,26,36,46,56,6
Calculate the probability of the following events A the first number is 2 or 3 or4 B P(A) P(B) P(not A) P(not B) P(A or B) the second number is 1 or 2 or 3 P(A and B) P(A given B) 2 Dice Sample Space 1,6 1,5 2,5 3,5 4,5 5,5 1,4 1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 2,6 3,6 4,6 2,4 3,4 4,4 5,4 6,4 5,6 6,5...
Calculate the probability of the following events A the first number is 2 or 3 or 4 E the second digit is 3 or less F the second digit is 4 or greater PIE or F) P(E and F) P(A) P( A and E) P( A and F) P( A and E)+P( Aand F) 2 Dice Sample Space 1,1 2,1 3,1 4,1 5,1 1,6 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,5 2,4 3,4 4,4...
Iculate the probability of the foltowing events G first digit 1, 2, or 3 P(F) P(G) | F-sum of digits-4 P(F and G) P(F given G) P(F and G)/P(G) 2 Dice Sample Space 1,6 2,6 3,6 1,5 1,1 2,1 3,1 4,1 5,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 2,5 3,5 4,5 4,6 5,5 5,6 6,5 6,6 6,1 25/2018 HW 2- Probability 1
An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space provided below and assuming each simple event is as likely as any other, find the probability that the sum of the dots is not 2 or 8. 1 5 (1,5) First Die (1,1) 2 (2.1) (3,1) 4 (4.1) (5,1) 6 (61) 2 (1,2) (2.2) (3,2) (4,2) (5,2) (6,2) لا لا ، الا ان Second Die 3 4 (1,3)...
A single 6-sided die is rolled twice. The set of 36 equally likely outcomes is {(1,1), (1,2), (1,3), (1,4), left parenthesis 1 comma 5 right parenthesis comma(1,5), left parenthesis 1 comma 6 right parenthesis comma(1,6),left parenthesis 2 comma 1 right parenthesis comma(2,1),left parenthesis 2 comma 2 right parenthesis comma(2,2),(2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3),left parenthesis 4 comma 4 right parenthesis comma(4,4),left parenthesis 4 comma 5 right parenthesis comma(4,5),left parenthesis 4 comma 6 right...
An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space provided below and assuming each simple event is as likely as any other, find the probability that the sum of the dots is 4. 1 5 (1,5) First Die (2.5) 1 (1,1) 2 (2.1) 3 (3.1) 4 (4.1) 5 (5.1) 6 (61) 2 (1,2) (2.2) (3,2) (4,2) (5,2) (6,2) Second Die 3 4 (1,3) (1.4) (2,3) (2.4) (3,3)...
2. [7 points) Find all the Nash equilibrium (pure and mixed strategies) in the following games. a) (2 points) column left middle right 5,2 2,1 1,3 4,0 1,-1 0,4 row up down 10 column left right b) [2 points] row L up 1,1 -1.0 down -1,0 1,1 c) [3 points] left 3,3 4,6 11,5 up middle down column middle right 9,4 5,5 | 0,0 6,3 5,4 0,7 row
The graphs below are used to answer parts b-e. Please help!! Trial Values of both dice Difference Win/Loss amount Example (8.6 (largest-smallest) 6-3 3 (3,6) $-2 S-2 $5 $-2 S-2 S-2 $-2 S-2 S-2 (5,6) 6-5-1 (3,6) (2,5) (2,6) (5,5) (5,2) 6-3-3 5-2-3 6-2-4 5-50 5-2-3 (6,5) (5,3) (4,2) (5,6) 6-5-1 5-3-2 4-2-2 6-5-1 $ 5 S-2 S-2 10 12 13 aBbC AaBbcal AaB AaB | | 1 Normal 1 No Spac Heading 1 Heading 2 Title Sub 0 x2...
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? What are the Nash equilibria of these games? (a) Player 2 Left 0,2 1,3 2,4 Top Middle Bottom Center 4,3 2,4 1,5 Right 3, 4 2, 3 4,6 Player 1 (b) Player 2 Left 2,4 3,3 4,6 Top Middle Bottom Center 6,5 4,3 5,4 Player 1 Right 5,3 4, 2 2,5