Question

you roll a 6 - sided die.
what is p(not divisor of 6)?
write your answer as a fraction or whole number.

Explanation:

Step1: Determine total outcomes

A 6 - sided die has 6 possible outcomes: \(1,2,3,4,5,6\). So \(n(S)=6\).

Step2: Find divisors of 6

Divisors of 6 from 1 - 6 are \(1,2,3,6\). So \(n(\text{divisors of }6) = 4\).

Step3: Calculate non - divisors

Number of non - divisors \(n(\text{not divisor of }6)=6 - 4=2\) (the non - divisors are 4 and 5).

Step4: Compute probability

Using the formula \(P(A)=\frac{n(A)}{n(S)}\), where \(A\) is the event of getting a non - divisor of 6. So \(P(\text{not divisor of }6)=\frac{2}{6}=\frac{1}{3}\).

Answer:

\(\frac{1}{3}\)