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)? 1/9 2/9 1/3 2/3

Explanation:

Step1: Calculate probability of first - spin red

The spinner has 3 equal sections. The probability of getting red on the first spin, $P(R_1)$, is $\frac{1}{3}$ since there is 1 red section out of 3 total sections.

Step2: Calculate probability of second - spin yellow

Since the spins are independent events, the probability of getting yellow on the second spin, $P(Y_2)$, is also $\frac{1}{3}$ as there is 1 yellow section out of 3 total sections.

Step3: Use multiplication rule for independent events

For independent events $A$ and $B$, $P(A\cap B)=P(A)\times P(B)$. Here, $A$ is the event of getting red on the first spin and $B$ is the event of getting yellow on the second spin. So $P(\text{red, then yellow}) = P(R_1)\times P(Y_2)=\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}$.

Answer:

$\frac{1}{9}$