you spin the spinner twice. what is the probability of landing on a divisor of 42 and then landing on a 3…

Explanation:

Step1: Find divisors of 42

The divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. Among the numbers on the spinner (2, 3, 4, 5), the divisors of 42 are 2 and 3. So there are 2 favorable outcomes out of 4 for the first - spin. The probability of landing on a divisor of 42 on the first spin, $P_1=\frac{2}{4}=\frac{1}{2}$.

Step2: Find probability of landing on 3 on second - spin

There is 1 '3' on the spinner with 4 total sections. So the probability of landing on 3 on the second spin, $P_2 = \frac{1}{4}$.

Step3: Use multiplication rule for independent events

Since the two spins are independent events, the probability of both events occurring is the product of their individual probabilities. $P = P_1\times P_2$. Substitute $P_1=\frac{1}{2}$ and $P_2=\frac{1}{4}$ into the formula: $P=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$