Question

Assume that a fair six-sided die is rolled 13 times, and the roll is called a success if the result is in {1,2,3,4}. What is the probability that there are exactly 4 successes or exactly 4 failures in the 13 rolls?

Answer 1

Answer:

The answer to the question is;

The probability that there are exactly 4 successes or exactly 4 failures in the 13 rolls is $\frac{715}{8192}$.

Step-by-step explanation:

The probability of success = 1/2 =

probability of failure  = 1/2

Since we have 4 success we then have 9 failures and the given probability can be solved as ₁₃C₄ × 1/2ⁿ×1/2¹³⁻ⁿ

Therefore  we have

₁₃C₄ × 1/2⁴×1/2⁹ =  715/8192

That is the probability that there are exactly 4 successes or exactly 4 failures in the 13 rolls = 715/8192.