1572
1336
1936
1972
P(7 or 8) = P(H)P(7 or 8 | H) + P(T)P(7 or 8 | T)
(head then sum on dice 7 or 8, tail then number on ticket 7 or 8)
= (1/2) * (6/36) + (1/2) * (2/9) = 1/12 + 1/9 = (3 + 4)/36 = 7/36 = 19/108
However, there's a mistake in calculation. Let's correct it:
P(H) = 1/2
P(T) = 1/2
If H, the sum is 7 or 8. There are 6 ways to get a sum of 7 ((1,6), (2,5), (3,4), (4,3), (5,2), (6,1)) and 5 ways to get a sum of 8 ((2,6), (3,5), (4,4), (5,3), (6,2)). Total outcomes = 36.
P(7 or 8 | H) = (6+5)/36 = 11/36
If T, the number is 7 or 8. There are 2 favorable outcomes (7, 8) out of 9 total outcomes.
P(7 or 8 | T) = 2/9
P(7 or 8) = P(H)P(7 or 8 | H) + P(T)P(7 or 8 | T) = (1/2)(11/36) + (1/2)(2/9) = 11/72 + 2/18 = 11/72 + 8/72 = 19/72
The given options are incorrect or the problem statement has some error. The calculated probability is 19/72.