You roll a pair of standard dice. Create the sample space for a single roll of the dice and use the sample space to compute the following probabilities. (5 points total. 1 pt. for each part of the question.) A. Create a sample space. B. P (getting a 1 on the first die or getting a 5 on the second die) C. P (sum of the dice = 10) D. P (getting a 3 on the second die given that you got a 2 on the first die) E. P (getting an odd number on the first die and a value greater than 4 on the second die)A. 1 2 3 4 5 6 1 ( 1 , 1 ) (1, 2 ) ( 1 , 3 ) (1, 4 ) (1,5) (1,6) 2 (2, 1 ) ( 2, 2 ) ( 21 3 ) ( 2, 4 ) (2, 5) (2, 6 ) 3 ( 3, 1) ( 3, 2) ( 3, 3 ) (3, 4 ) (31 5 ) ( 3, 6 ) 4 ( 4, 1 ) ( 4, 2) ( 4 , 3) ( 4, 4 ) ( 415 ) ( 4 , 6 ) 5 ( 5, 1 ) ( 5, 2 ) (5, 3 ) 5, 4 ) ( 5 , 5) ( 516 ) 6 ( 6,1) ( 61 2) ( 61 3) ( 6, 4 ) (6, 5 ) ( 6 , 6) b. ) A = getting a 1 on the first clie B = getting a 5 on the second die P(AUB ) = P(A) + P(B) - P(AnB) P(A) = 1/6 P(B ) = 1/6 P ( An B ) = ( 1 16) ( 1 16 ) = 1/36 P ( AorB) = 116+ 116 - 1/36 = 11/ 36 = 0.3056 = 30. 56% C. ) 4 + 6 = 10 4 + 4 = 10 3 ways to make sum 10, Sample SPCIce = 36 5+5 = 10 possible outcomes P ( sum of the dice = 10) = 3/36 = 0.0833 = 8.3390 D. ) 6 possible outcomes to get 2 on the First clie ( 2, 3 ) = 1 way to have both 2 on the first clie and 3 on the second die. P (3 on second clic; 2 on the first die) = 1/6) = 0.1467 = 16.67% E. ) A= getting an odd number on the first die B= value greater than 4 on the second die P (A and B) = P(A) * P(B) P(A) = 316 P (B) = 216 = 1/3 P ( A and B) = ( 316 ) ( 1/3) = 3/ 18 = 1/6) = 0.1667= 16.67%