Question

you spin the spinner twice.
what is the probability of landing on a prime number and then landing on a prime
number?
simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Determine prime numbers on spinner

Prime numbers among \(6,7,8,9\) are \(7\). So probability of landing on prime number in one spin is \(\frac{1}{4}\).

Step2: Use multiplication rule for independent events

Since spins are independent, probability of landing on prime number twice is \(\frac{1}{4}\times\frac{1}{4}\).
$$\frac{1}{4}\times\frac{1}{4}=\frac{1\times1}{4\times4}=\frac{1}{16}$$

Answer:

\(\frac{1}{16}\)