Question - Calculating Probability of Landing on Prime Number and Divisor of 3
Solution:
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 sectionsP(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 sectionsP(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 * 1/2P(combined) = 1/4To 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%.
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