Suppose that you roll a pair of 16sided dice with the sides

Suppose that you roll a pair of 16-sided dice (with the sides numbered 1-16) a total of 200 times. What is the probability that you will get a sum of 3 at least two times?

Solution

We need to get the probability of getting number 3 on the dice atleast 2 times or more

= 1 - P ( getting 3, at max 1)

= 1 - P (X=0) - P (X=1)

Probability of success = 2 / 256

Probability of failure = (254 / 256)

P(X=0) i.e getting 3 zero times in 200 runs = ²⁰⁰C₀ ( 2 / 256)⁰ (254 / 256)²⁰⁰ =0.208329

P(X=1) i.e getting 3 one times in 200 runs = ²⁰⁰C₁ ( 2 / 256)¹ (254 / 256)¹⁹⁹ =0.328077

Thus,

Required probability = 1 - (0.208329 + 0.328077)

= 0.46359

Hope this helps. Ask if you have any doubts.