Two fair dice are tossed. Let A be the event that the sum of the values which co

Question

Two fair dice are tossed. Let A be the event that the sum of the values which come up is 6, B be the event that the first die comes up 3, and C be the event that the total of the values which come up is 10. Find, by counting outcomes in the sample space if necessary, P(A) P(B) P(C) P(A B) P(B C) A license plate consists of 3 letters followed by 4 digits. (A digit is one of 0 1,, 9.) How many possible license plates are there? Assume letters may be repeated, digits may be repeated, and all combinations are allowed.

Explanation / Answer

(1)
Total number of cases for two dice in a sample space = 36
For sum of values = 6, the elements can be = {(1,5), (5,1), (2,4), (4,2), (3,3)}
hence set A = {(1,5), (5,1), (2,4), (4,2), (3,3)}

For first die having 3, the elements can be = {(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)}
hence set B = {(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)}

For sum values = 10, the elements can be = {(4,6), (6,4), (5,5)}
hence set C = {(4,6), (6,4), (5,5)}
intersection of A and B gives = {(3,3)}
intersection of B and C gives = (null set)
(a) P(A) = 5/36
(b) P(B) = 6/36 = 1/6
(c) P(C) = 3/36 = 1/12
(d) P(A intersection B) = 1/36
(e) P( A intersection C) = 0
(f) P(B bar) = 1 - P(B) = 1 - 1/6 = 5/6
(3)
3 letters can be selected in = 26C3 ways
4 digits can be selected in = 10C4 ways
total number of plates = 26C3 x 10C4

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