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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?

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alissastrom6
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

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

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

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

[tex] 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 [/tex]

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