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vladimir2022 [97]
3 years ago
5

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 wil

l give a result that is not a prime number?
Mathematics
2 answers:
bekas [8.4K]3 years ago
8 0

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

Rasek [7]3 years ago
8 0
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
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