Question

you spin the spinner twice.

what is the probability of landing on a prime number and then landing on a 1?

write your answer as a percentage rounded to the nearest tenth.

%

Explanation:

Step1: Determine prime numbers on spinner

Prime numbers on spinner: \(2,3,5,7\). There are \(4\) prime numbers. Total numbers on spinner \(n = 8\). Probability of landing on prime number \(P(\text{prime})=\frac{4}{8}=\frac{1}{2}\)

Step2: Probability of landing on 1

There is \(1\) section with \(1\). Probability of landing on \(1\) \(P(1)=\frac{1}{8}\)

Step3: Use multiplication rule for independent events

Since spins are independent, \(P(\text{prime then }1)=P(\text{prime})\times P(1)\)
\(P=\frac{1}{2}\times\frac{1}{8}=\frac{1}{16}\)

Step4: Convert to percentage

\(\frac{1}{16}=0.0625\). To convert to percentage, multiply by \(100\). \(0.0625\times100 = 6.25\%\approx6.3\%\)

Answer:

\(6.3\)