Question

you spin the spinner twice. what is the probability of landing on a prime number and then landing on a prime number? write your answer as a percentage rounded to the nearest tenth.

Explanation:

Step1: Identify prime numbers

The prime numbers on the spinner are 2, 3, 5, 7. There are 4 prime numbers out of 6 total numbers.

Step2: Calculate first - spin probability

The probability of landing on a prime number on the first spin is $P_1=\frac{4}{6}=\frac{2}{3}$.

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 $P_2 = \frac{4}{6}=\frac{2}{3}$.

Step4: Calculate combined probability

The probability of both events occurring is $P = P_1\times P_2=\frac{2}{3}\times\frac{2}{3}=\frac{4}{9}$.

Step5: Convert to percentage

$P=\frac{4}{9}\approx0.4444$. As a percentage, $0.4444\times100 = 44.4\%$.

Answer:

44.4%