Question

you spin the spinner twice.
what is the probability of landing on a number less than 4 and then landing on a divisor of 81?
simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Calculate the probability of landing on a number less than 4

Numbers less than 4 are 2 and 3. There are 3 numbers on the spinner. So the probability \(P_1=\frac{2}{3}\)

Step2: Calculate the probability of landing on a divisor of 81

Divisors of 81: 1, 3, 9, 27, 81. On the spinner, the number 3 is a divisor. So the probability \(P_2 = \frac{1}{3}\)

Step3: Calculate the combined probability

Since the two spins are independent events, use the formula \(P = P_1\times P_2\). So \(P=\frac{2}{3}\times\frac{1}{3}=\frac{2}{9}\)

Answer:

\(\frac{2}{9}\)