you spin the spinner once. what is p(even or greater than 2)? write your answer as a percentage. %

Explanation:

Step1: Identify the sample space and individual probabilities.

The spinner has three equally likely outcomes: 2, 3, and 4. The sample space $S = {2, 3, 4}$. The probability of landing on each number is: $P(2) = \frac{1}{3}$ $P(3) = \frac{1}{3}$ $P(4) = \frac{1}{3}$

Step2: Define the events.

Let A be the event that the spinner lands on an even number. The even numbers are 2 and 4. So, event $A = {2, 4}$. Let B be the event that the spinner lands on a number greater than 2. The numbers greater than 2 are 3 and 4. So, event $B = {3, 4}$.

Step3: Determine the outcomes for the event "even or greater than 2".

We are looking for the probability $P(A \text{ or } B)$, which is $P(A \cup B)$. The outcomes in $A \cup B$ are the elements that are in A, or in B, or in both. $A \cup B = {2, 4} \cup {3, 4} = {2, 3, 4}$.

Step4: Calculate the probability of the event "even or greater than 2".

The probability of $A \cup B$ is the sum of the probabilities of the outcomes in $A \cup B$. $P(A \cup B) = P(2) + P(3) + P(4)$ $P(A \cup B) = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = \frac{3}{3} = 1$

Alternatively, using the formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$: $P(A) = P(2) + P(4) = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}$ $P(B) = P(3) + P(4) = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}$ The event $A \cap B$ is "even and greater than 2", which is the outcome {4}. $P(A \cap B) = P(4) = \frac{1}{3}$ $P(A \cup B) = \frac{2}{3} + \frac{2}{3} - \frac{1}{3} = \frac{4-1}{3} = \frac{3}{3} = 1$

Step5: Convert the probability to a percentage.

To express the probability as a percentage, multiply by 100. Percentage = $1 \times 100%$

Answer:

$100%$