A spinner is divided into three equal parts: red, blue, and green. Hayley spins the spinner twice. What is the probability that she will not land on blue in either spin?

1. Problem Description

A spinner is divided into three equal parts: red, blue, and green. Hayley spins the spinner twice. What is the probability that she will not land on blue in either spin?

2. Solution Steps

The spinner has three equal parts, red, blue, and green.

The probability of landing on blue in a single spin is $\frac{1}{3}$.

The probability of not landing on blue in a single spin is $1 - \frac{1}{3} = \frac{2}{3}$.

Since Hayley spins the spinner twice, and the spins are independent events, the probability of not landing on blue in either spin is the product of the probabilities of not landing on blue in each individual spin.

Probability of not landing on blue in either spin = (Probability of not landing on blue in the first spin) * (Probability of not landing on blue in the second spin)

So, the probability is $\frac{2}{3} \times \frac{2}{3} = \frac{4}{9}$.

3. Final Answer

The probability that she will not land on blue in either spin is $\frac{4}{9}$.