you spin the spinner twice. what is the probability of landing on an odd number and then landing on an odd…

Explanation:

Step1: Count odd - numbered sections

There are 4 odd - numbered sections (3, 5, 7, 9) out of 8 total sections. So the probability of landing on an odd number on the first spin is $\frac{4}{8}=\frac{1}{2}$.

Step2: Calculate probability of second spin

Since the spins are independent events, the probability of landing on an odd number on the second spin is also $\frac{4}{8}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

The probability of two independent events A and B occurring is $P(A)\times P(B)$. Here, $P(A) = P(B)=\frac{1}{2}$, so the probability of landing on an odd number and then landing on an odd number is $\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$