Question

Sam intends to roll a six sided cube 100 times. What is the probability model he can use to predict whether or not each roll will give a result that is not a prime number?

Answer 1

The outcomes of rolling fair six sided die is $\{1,2,3,4,5,6\}$. The prime numbers in the above outcomes are $\{2,3,5\}$. The probability of not rolling a prime number is $p=\frac{3}{6}= 0.5$.

Each trial is independent.

In the given experiment of 100 trials, the binomial probability model can be used to predict the number of occurrence of non-prime numbers (X). The probability mass function is

$P(X=x)=C(100,x)p^x(1-p)^{100-x},x=0,1,2,3,...,100$. Since $p=0.5,1-p=0.5$

$P(X=x)=C(100,x)0.5^x(0.5)^{100-x},x=0,1,2,3,...,100 \\ P(X=x)=C(100,x)(0.5)^{100},x=0,1,2,3,...,100$

Answer 2

It’s 0.5 probability chance because it is still the same cube being used for the probability of it landing on a prime number