Question

a spinner has three equal sections labeled 1, 2, and 3. it is spun twice. which expression can be used to determine p(2, then 1)?

Explanation:

Step1: Calculate probability of first - spin result

The spinner has 3 equal - sections. The probability of getting a 2 on the first spin is $\frac{1}{3}$ because there is 1 section labeled 2 out of 3 total sections.

Step2: Calculate probability of second - spin result

Since the spins are independent events, the probability of getting a 1 on the second spin is also $\frac{1}{3}$ as there is 1 section labeled 1 out of 3 total sections.

Step3: Use the multiplication rule for independent events

For independent events $A$ and $B$, $P(A\text{ and }B)=P(A)\times P(B)$. Here, $A$ is the event of getting a 2 on the first spin and $B$ is the event of getting a 1 on the second spin. So $P(2,\text{ then }1)=\frac{1}{3}\times\frac{1}{3}$.

Answer:

$\frac{1}{3}\cdot\frac{1}{3}$