Answer:
The probability that sum of numbers rolled is a multiple of 3 or 4 is: [tex]\frac{7}{12}[/tex].
Step-by-step explanation:
The sample space for two fair die (dice) is given below:
[tex]\left[\begin{array}{ccccccc}&1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right][/tex]
From the above table:
Number of occurrence where sum is multiple of 3 = 12
Number of occurrence where sum is multiple of 4 = 9
Total number in the sample space = 36
probability(sum is 3) = 12/36
probability(sum is 4) = 9/36
probability(sum is 3 or 4) [tex]=\frac{12}{36} +\frac{9}{36} \\=\frac{12 + 9}{36} \\=\frac{21}{36}\\=\frac{7}{12}[/tex]
