Question

you spin the spinner twice.
what is the probability of landing on a factor of 10 and then landing on a factor of 54?
write your answer as a decimal rounded to the nearest thousandth.

Explanation:

Step1: Find factors and probability for first spin

Factors of \(10\) are \(5\). There are \(4\) sections on the spinner. Probability of landing on \(5\) (a factor of \(10\)) is \(P_1=\frac{1}{4}\).

Step2: Find factors and probability for second spin

Factors of \(54\) are \(6\). Probability of landing on \(6\) (a factor of \(54\)) is \(P_2 = \frac{1}{4}\).

Step3: Use multiplication rule for independent events

Since the two spins are independent events, the probability \(P=P_1\times P_2\). Substitute \(P_1=\frac{1}{4}\) and \(P_2=\frac{1}{4}\), we get \(P=\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}\).

Step4: Convert to decimal

\(\frac{1}{16}=1\div16 = 0.0625\approx0.063\) (rounded to the nearest thousandth).

Answer:

\(0.063\)