Suppose that you roll a pair of 24sided dice with the sides

Suppose that you roll a pair of 24-sided dice (with the sides numbered 1-24) a total of 500 times. What is the probability that you will get a sum of 4 at least two times? Please show all work.

Solution

There are 24*24 = 576 different outcomes.

There are only 2 possibilities with a sum of 3: (1,2) and (2,1).

Thus, the probability of getting a sum of 3 = 2/576 = 0.003472222.

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 =    200      
p = the probability of a success =    0.003472222      
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   ) =    0.846308821
          
Thus, the probability of at least   2   successes is  
          
P(at least   2   ) =    0.153691179 [ANSWER]