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: Find probability of first - spin being 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: Find probability of second - spin being yellow

Since the spins are independent events, after the first spin, the conditions remain the same for the second spin. The probability of getting yellow on the second spin, $P(Y_2)$, is $\frac{1}{3}$ 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:

$\frac{1}{9}$