Question

you roll a 6 - sided die. what is p(4 or prime)? write your answer as a percentage rounded to the nearest tenth.

Explanation:

Step1: Identify total outcomes

A 6 - sided die has 6 possible outcomes, so $n(S)=6$.

Step2: Identify prime numbers on a 6 - sided die

The prime numbers on a 6 - sided die are 2, 3, 5. So the set of prime numbers $A=\{2,3,5\}$ and $n(A) = 3$. The number 4 is another outcome we are interested in. Let $B = \{4\}$ and $n(B)=1$.

Step3: Use the formula for $P(A\cup B)$

The formula for the probability of the union of two non - mutually exclusive events $P(A\cup B)=\frac{n(A)+n(B)}{n(S)}$. Here, $n(A\cup B)=n(A)+n(B)$ since 4 is not a prime number. So $n(A\cup B)=3 + 1=4$.

Step4: Calculate the probability

$P(A\cup B)=\frac{4}{6}=\frac{2}{3}$.

Step5: Convert to percentage

$\frac{2}{3}\times100\%\approx66.7\%$

Answer:

$66.7\%$