Question

you spin the spinner twice. what is the probability of landing on a factor of 90 and then landing on a number greater than 4? simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Find factors of 90 on spinner

The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. On the spinner, the factors of 90 are 2, 3, 5, 6. So there are 4 favorable outcomes out of 8 for the first - spin. The probability of landing on a factor of 90 on the first spin is $P_1=\frac{4}{8}=\frac{1}{2}$.

Step2: Find numbers greater than 4 on spinner

The numbers greater than 4 on the spinner are 5, 6, 7, 8. So there are 4 favorable outcomes out of 8 for the second - spin. The probability of landing on a number greater than 4 on the second spin is $P_2=\frac{4}{8}=\frac{1}{2}$.

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. So $P = P_1\times P_2$. Substitute $P_1=\frac{1}{2}$ and $P_2=\frac{1}{2}$ into the formula: $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$