Calculating Probability of Landing on Prime Number and Divisor of 3
To solve this problem, we will calculate the probability of landing on a prime number on the first spin and then multiply that by the probability of landing on a divisor of 3 on the second spin.
The spinner has 4 sections: 2, 3, 4, and 1. The prime numbers on the spinner are 2 and 3.
The probability of landing on a prime number on the first spin is the number of prime number sections divided by the total number of sections:
P(prime number) = number of prime number sections / total number of sections
P(prime number) = 2/4 since both 2 and 3 are prime numbers and there are 4 sections in total.
Now, we calculate the probability of landing on a divisor of 3 on the second spin. The divisors of 3 on the spinner are 1 and 3.
The probability of landing on a divisor of 3 on the second spin is:
P(divisor of 3) = number of sections that are divisors of 3 / total number of sections
P(divisor of 3) = 2/4 because both 1 and 3 are divisors of 3.
The combined probability of both events happening in sequence (landing on a prime number first, and then a divisor of 3) is given by multiplying the probabilities of each event:
P(combined) = P(prime number) * P(divisor of 3)
P(combined) = (2/4) * (2/4)
P(combined) = 1/2 * 1/2
P(combined) = 1/4
To express this probability as a percentage rounded to the nearest tenth, we convert the fraction to a decimal and then to a percentage:
P(combined) in decimal = 0.25 (since 1/4 is equivalent to 0.25)
Now as a percentage:
P(combined) as a percentage = 0.25 * 100%
P(combined) as a percentage = 25%
Rounded to the nearest tenth, it remains 25.0%.
Therefore, the probability of landing on a prime number and then landing on a divisor of 3, when expressed as a percentage rounded to the nearest tenth, is 25.0%.
