you spin both spinners. what is the probability of spinning a on the first spinner and an even number on the…

Explanation:

Step1: Calculate probability of spinning A

The first spinner has 2 equal - sized sections (A and B). The probability of spinning A, denoted as $P(A)$, is $\frac{1}{2}$ since there is 1 favorable outcome (A) out of 2 total outcomes.

Step2: Calculate probability of spinning an even number

The second spinner has 3 equal - sized sections (1, 2, 3). The even number is 2, so there is 1 favorable outcome out of 3 total outcomes. The probability of spinning an even number, denoted as $P(\text{even})$, is $\frac{1}{3}$.

Step3: Use the multiplication rule for independent events

Since the spins of the two spinners are independent events, the probability of both events occurring is the product of their individual probabilities. So $P(A\text{ and even})=P(A)\times P(\text{even})$. $P(A)\times P(\text{even})=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$

Answer:

$\frac{1}{6}$