2- (25 points) Two standard 6-sided dice with 6 faces having vatues (1,2.3,4,5.6

Question

2- (25 points) Two standard 6-sided dice with 6 faces having vatues (1,2.3,4,5.6) are thrown and the f values on the top face of each die are observed. Optional: Illustra te the sample space S of this random experiment clearly showing all possible outcomes Let H be the event that the sum of the dice face values is even, let I be the event that none of the dice lands c the values 1,2,or 3, let K be the event that the two face values are equal. Assume equally likely outcomes an find the probabilities below and indicate if any of them are greater than 1.0 P(H) = P(I) = P(K)- p(H11) = PCHIK) P(IK) = P(OH)

Explanation / Answer

s = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

  (2,1), (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), (4,4), (4,5), (4,6),

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

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

H = {(1,1), (1,3), (1,5), (2,2), (2,4), (2,6),

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

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

I = {(4,4), (4,5), (4,6),

(5,4), (5,5), (5,6),

(6,4), (6,5), (6,6)}

K = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}

P(H) = 1/2 = 0.5

P(I) = 9/36 = 1/4 = 0.25

P(K) = 6/36 = 1/6

P(H|I) = 5/9

P(H|K) = 6/6 = 1

P(I|K) = 3/6 = 1/2 = 0.5

P(I|H) = 5 / 18

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