Question

a spinner contains 3 equal sections: one red, one yellow, and one blue. the possible results of two spins are shown in the tree diagram below. what is p(red, then yellow)?
(\frac{1}{9}) (\frac{2}{9}) (\frac{1}{3}) (\frac{2}{3})

Explanation:

Step1: Find P(red first)

The spinner has 3 equal sections, so the probability of landing on red first is $P(\text{red}) = \frac{1}{3}$.

Step2: Find P(yellow second)

After the first spin (regardless of the result), the spinner still has 3 equal sections. So the probability of landing on yellow second is $P(\text{yellow}) = \frac{1}{3}$.

Step3: Multiply the probabilities

Since the two spins are independent events, we multiply the probabilities: $P(\text{red, then yellow}) = P(\text{red}) \times P(\text{yellow}) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$.

Answer:

$\frac{1}{9}$