I need 1 and 2 with a good handwriting please. 1. Two six-sided dice will be rol

Question

I need 1 and 2 with a good handwriting please.

1. Two six-sided dice will be rolled once and the numbers (number of dots) on each dice is to be recorded. Define events E,-the sum of the two dice is i, i = 2,3, , 12. a. List all the outcomes in the Sample Space. b. Calculate the probability of each event, E, , , E12- c. Let A be the event "the sum of the two dice is greater than 6". Calculate P(E10IA) and P(AlE10) Note: this is Conditional Probability notation found in section 1.3 of your text. 2. Consider the experiment described in question 1 Let A = the sum of the two dice is greater than 6 And let B = the sum of the two dice is a prime number. Calculate and compare both sides of De Morgan's Laws:

Explanation / Answer

a All the possible outcomes will be some of the no. on both dice (1 to 6)

means like (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

similarly

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

SO total outcomes of all sample space=2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12

b)

E2=1/36 (AS THERE ARE THIRTY SIX OUTCOMES)

E3=2/ 36=1/18 (2 appears twice in the sample space)

E4=3/36=1/12

E5=4/36=1/9

E6=5/36

E7=6/36=1/6

E8=7/36

E9=8/36=2/9

E10=9/36=1/4

E11=10/36=5/18

E12=11/36

C) P (E10/A)=Probability of E10 after the occurence of A =P(E10)/P(A)

where A is the sum of the two dice greater than 6 =21cases

P(E10) will be the cases like(4,6)(6,4)(5,5)

so P(E10/A)=3/21=1/7

P(A/E10)=PROBABILITY OF A after the occurence of E10

=3/3=1

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