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Stat 352 Homework Set 2 Fall 2019: Conditional Probability and Independence Deadline: Monday November 11, 2019 (1) In throwing two dice with the sample space Define the following events on : 1,2,3,4, 5,6}. {(x, y): x, y = A={sum less than 4) {(x, y): x + y < 4, x,y = 1,2,3,4,5,6} first number is 1) = {(x, y): x = 1, C = {sum of number is 5} = {(x, y): x + y = 5, x, y = 1,2,3,4,5,6} D = {numbrs are not the same} = {(x, y): x # y, Numbers are the same} = {(x, y): x = y, x, y = 1,2,3,4,5,6} B = y = 1,2,3,4,5,6} x, y 1,2,3,4,5,6} E = Calculate: (i) P(E), (ii) P(E), (iii) P(A B) (iv) P(C : D), P(AIB)?

Answer 1

Given, sample space 2= {(x,y); x, Y = 1, 2, 3, 4,5,6} &n (-2)=36=n. and events define on s dise A = {sum tess than 4} = {(x,y); x+y<4, X,4=1,2,3,4,56} B={fiest number is 13 = {(x,y); x= 1, y=1,2,3,4,5,6} C={sum of number is 53={(x,y): X+Y=5, ,4=1,2,3,4,5,6}| D={numbers are not the same}={(x,y); x+y , 2,Y=1,2,3,4,5,6}} E={ numbers are the Same} ={(x,y);=4,X,Y=12,3,4,5,63 1) PCE) = h a em={(1,1),(2,2), (3,3),(4,4),(5,5), 1:) P(E)= 1 –P() = 1-1-15 (6,6)}

ii) P(AB) = ? AB = {sum less than 4 and first number is 1} = $6,y); x+y <h and x=1,4=1,2,3,4,5,6} * (:B)={.(,1),(1, 2)} & (A:B) = 2 :: P(4:B) = iv) PLC:D) = ?,P(A/B) = ? fiostly P(6:0) = ? B CED={sum of number is 58 and numbers are not the same} =>(a,y); x+y and x+y = 5, X, Y = 1,2,3,4,5,63 = {(1,4), (2,3), (4,1), (3, 2)} ((:D) = 4 P((:D) = PC: D) - n() and Now P(A/B) = f(708). (7698) s=4 - 3 P(B) n(B) where, A = { sum greater than an equal to 43 = {(x,y): x+Y>, 4 , &,9 = 1, 2, 3, 4,5,63 ĀAB= {(x,y); aty 34 and a=1, 9=1, 2, 3, 4,5,63 : BĀ (B)={(1,3),(1,5),(1,6),(1,4)} LAB)= 4 B={(1, 1), (1, 2), (1, 3), (1,4), (1,5), (1,5)} = n(B) = 6