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

Explanation:

Step1: Identify prime numbers on spinner

The prime numbers on the spinner are 2, 3, 5, 7. There are 4 prime numbers out of 8 total numbers.

Step2: Calculate first - spin probability

The probability of landing on a prime number on the first spin is the number of prime numbers divided by the total number of outcomes. So, $P_1=\frac{4}{8}=\frac{1}{2}$.

Step3: Calculate second - spin probability

Since the spins are independent events, the probability of landing on a prime number on the second spin is also $P_2 = \frac{4}{8}=\frac{1}{2}$.

Step4: Calculate combined probability

For independent events, the probability of both events occurring is the product of their individual probabilities. So, $P = P_1\times P_2=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$