Question

you spin the spinner twice. what is the probability of landing on a prime number and then landing on a number greater than 5? simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Identify prime numbers

Prime numbers among 5, 6, 7, 8 are 5 and 7. So probability of landing on prime number first, $P_1=\frac{2}{4}=\frac{1}{2}$.

Step2: Identify numbers greater than 5

Numbers greater than 5 among 5, 6, 7, 8 are 6, 7, 8. So probability of landing on number greater than 5 second, $P_2=\frac{3}{4}$.

Step3: Calculate combined probability

Since the two spins are independent events, the combined probability $P = P_1\times P_2$. So $P=\frac{1}{2}\times\frac{3}{4}=\frac{3}{8}$.

Answer:

$\frac{3}{8}$