you spin the spinner twice. what is the probability of landing on a 7 and then landing on an even number…

Explanation:

Step1: Find probability of landing on 7

The spinner has 5 sections. The probability of landing on 7 in the first - spin is $P(7)=\frac{1}{5}$ since there is 1 section labeled 7 out of 5 total sections.

Step2: Find probability of landing on an even number

The even - numbered sections are 6 and 8. So there are 2 even - numbered sections out of 5 total sections. The probability of landing on an even number in the second spin is $P(\text{even})=\frac{2}{5}$.

Step3: Use the multiplication rule for independent events

Since the two spins are independent events, the probability of both events occurring is the product of their individual probabilities. So $P(7\text{ then even})=P(7)\times P(\text{even})$. $P(7)\times P(\text{even})=\frac{1}{5}\times\frac{2}{5}=\frac{2}{25}$

Answer:

$\frac{2}{25}$