you spin the spinner twice. what is the probability of landing on a number greater than 4 and then landing…

Explanation:

Step1: Identify numbers greater than 4

The numbers on the spinner are 4, 5, 6, 7. The numbers greater than 4 are 5, 6, 7. So there are 3 numbers greater than 4 out of 4 total numbers. The probability of landing on a number greater than 4 in the first - spin, $P_1=\frac{3}{4}$.

Step2: Identify prime numbers

The prime numbers on the spinner are 5, 7. So there are 2 prime numbers out of 4 total numbers. The probability of landing on a prime number in the second - spin, $P_2=\frac{2}{4}$.

Step3: Calculate the combined probability

Since the two spins are independent events, the probability of both events occurring is the product of their individual probabilities. $P = P_1\times P_2=\frac{3}{4}\times\frac{2}{4}=\frac{6}{16}$.

Step4: Convert to percentage

To convert $\frac{6}{16}$ to a percentage, we calculate $\frac{6}{16}\times100% = 37.5%$.

Answer:

37.5%