Success or failures in rolling a fair die

Question

This deals with rolling a fair die. Assume that the die is rolled 13 times, and the roll is called a success if the result is in { 1, 2, 3 }. What is the probability that there are exactly 2 successes or exactly 2 failures in the 13 rolls?

Answer 1

The probability of success is 3/6 = 1/2. 

The probability of failure is also 1/2.

 

So you need exactly 2 successes which leaves you over with 11 failures. And out of the 13 tries, you need to choose the 2 that are successes......so

 

₁₃C₂ *(1/2)² * (1/2)¹¹ is your answer.....= 78/2048.

 

Hope this helped.