Calculating Probability of Spinner Events
To solve this probability problem, we need to identify the prime numbers and the divisors of 3 from the spinner, and then calculate the probability of these two events occurring in sequence when the spinner is spun twice.
First, let's identify the prime numbers on the spinner. Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. From the spinner, we can see that the numbers are 2, 3, and 4. Among these, 2 and 3 are prime numbers.
Second, we need to identify the divisors of 3. A divisor of a number is an integer that can divide the number without leaving a remainder. The number 1 and the number itself (in this case, 3) are always divisors of the number. So, the divisors of 3 on the spinner are 1 and 3.
Now let's calculate the probabilities:
- The probability of landing on a prime number (2 or 3) in the first spin is the number of prime numbers on the spinner divided by the total number of sections on the spinner. There are 2 prime numbers (2 and 3) and a total of 4 sections, so this probability is 2/4 or 1/2.
- The probability of landing on a divisor of 3 (1 or 3) in the second spin is the number of divisors of 3 on the spinner divided by the total number of sections on the spinner. Since there are 2 divisors of 3 (1 and 3) out of 4 sections, this probability is also 2/4 or 1/2.
To find the overall probability of both events occurring in sequence (landing on a prime number first and then on a divisor of 3), we multiply the probabilities of each individual event:
Probability of prime number AND divisor of 3 = (1/2) * (1/2) = 1/4
To express this as a percentage rounded to the nearest tenth, multiply by 100 and round:
1/4 * 100% = 25%
Thus, the probability of landing on a prime number and then landing on a divisor of 3, when you spin the spinner twice, is 25%.
