the spinner is equally likely to land on any of the six sections. what is the probability that the spinner…

Explanation:

Step1: Define events

Let $A$ be the event that the spinner lands on a number greater than 4. So $A={5,6}$. Let $B$ be the event that the spinner lands on a shaded - section. So $B = {1,3,5}$.

Step2: Calculate probabilities of individual events

The probability of an event $E$ in a sample - space $S$ with $n(S)$ equally - likely outcomes and $n(E)$ favorable outcomes is given by $P(E)=\frac{n(E)}{n(S)}$. Here, $n(S) = 6$. $P(A)=\frac{2}{6}$ since $n(A)=2$. $P(B)=\frac{3}{6}$ since $n(B)=3$.

Step3: Calculate the intersection of events

$A\cap B={5}$, so $P(A\cap B)=\frac{1}{6}$ since $n(A\cap B)=1$.

Step4: Use the addition rule of probability

The addition rule of probability for two events $A$ and $B$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. $P(A\cup B)=\frac{2}{6}+\frac{3}{6}-\frac{1}{6}=\frac{2 + 3-1}{6}=\frac{4}{6}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$