Suppose that you roll a pair of 14sided dice with the sides

Suppose that you roll a pair of 14-sided dice (with the sides numbered 1-14) a total of 53 times. What is the probability that you will get a sum of 27 at least twice?

Solution

There are 14^2 = 196.

Now, there are just 2 results that will give a 27: (13,14) and (14,13).

Thus,

p = 2/196 = 0.010204082

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    53      
p = the probability of a success =    0.010204082      
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   1   ) =    0.897923683
          
Thus, the probability of at least   2   successes is  
          
P(at least   2   ) =    0.102076317 [ANSWER]