Question

you spin the spinner twice.
what is the probability of landing on a number greater than 7 and then landing on a prime number?
write your answer as a decimal rounded to the nearest thousandth.

Explanation:

Step1: Determine the number of favorable outcomes for the first spin

Numbers greater than 7 on the spinner are 8 and 9. So there are 2 favorable outcomes. The total number of outcomes on the spinner is 5. The probability of landing on a number greater than 7, \(P(A)=\frac{2}{5}\)

Step2: Determine the number of favorable outcomes for the second spin

Prime numbers on the spinner: 5, 7. So there are 2 favorable outcomes. The probability of landing on a prime number, \(P(B)=\frac{2}{5}\)

Step3: Use the multiplication rule for independent events

Since the two spins are independent events, the probability of both events occurring is \(P(A\cap B)=P(A)\times P(B)\)

$$
LATEXBLOCK0
$$

Answer:

\(0.160\)