You spin the spinner twice.

Question

567

What is the probability of landing on a factor of 18 and then landing on a divisor of 72?

Simplify your answer and write it as a fraction or whole number.

Answer 1

To solve this problem, we need to first identify the factors of 18 and the divisors of 72.

Step 1: Find the factors of 18.

The factors of 18 are the numbers that can be multiplied together to get 18. These numbers are: 1, 2, 3, 6, 9, 18.

So, the factors of 18 are: $$1,2,3,6,9,18$$

Step 2: Find the divisors of 72.

The divisors of 72 are the numbers that can divide 72 without leaving a remainder. The divisors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

So, the divisors of 72 are: $$1,2,3,4,6,8,9,12,18,24,36,72$$

Step 3: Calculate the total outcomes.

Assuming the spinner has equally spaced numbers from which we can land, and each spin is independent, let's find the number of outcomes.

If the spinner allows for each of the factors of 18 and divisors of 72 to be counted in the total outcomes, we assume suitable ranges of values. However, since we need specific outcomes, let's see numbers of factors/divisors we got:

• Total distinct factors available for the first spin (related to 18) = 6
• Total distinct divisors available for the second spin (related to 72) = 12

Thus, the total number of outcomes when the spinner is spun twice is: $$\text{Total Outcomes}=6\text{ (for 18)}\times 12\text{ (for 72)}=72$$

Step 4: Probability calculation.

Now we calculate the probability of landing on a factor of 18 and then a divisor of 72. Each selected factor for 18 is independent from the selection of divisors for 72, so:

1. Probability of landing on a factor of 18: $$P(\text{Factor of 18})=\frac{6}{\text{Total Outcomes where Factor of 18 can be selected}}$$

2. Probability of landing on a divisor of 72: $$P(\text{Divisor of 72})=\frac{12}{\text{Total Outcomes where Divisor of 72 can be selected}}$$

The total outcomes again assumed equal weight so;

Next step, Total ways of landing (factors +divisors ) Would simply allow to calculate the probability as we sum the favorable outcomes that satisfy this condition.

Final Calculation: Thus, simply because every factor and divisor represents potential outcomes, Probability of both events occurring (factor of 18 first and divisor of 72 second) is calculated as: $$P(\text{Factor of 18 and Divisor of 72})=\frac{6\times 12}{Totalpossibleoutcomes}\Rightarrow =\frac{72}{72\times 72}=\frac{1}{12}$$

Thus, the final simplified answer for the probability of landing on a factor of 18 followed by a divisor of 72 is:

$$\boxed{{\displaystyle \frac{1}{12}}}$$