Question

1. spinner x is divided into 4 equal sections, and spinner y is divided into 3 equal sections. the possible outcomes for each spinner are shown in the tree diagrams. both spinners are spun at the same time. what is the probability that spinner x will land on 2 and spinner y will land on blue? a $\frac{7}{12}$ b $\frac{1}{12}$ c $\frac{2}{7}$ d $\frac{1}{2}$

Explanation:

Step1: Find P(X lands on 2)

Spinner X has 4 equal sections, so $P(X=2) = \frac{1}{4}$

Step2: Find P(Y lands on Blue)

Spinner Y has 3 equal sections, so $P(Y=\text{Blue}) = \frac{1}{3}$

Step3: Calculate joint probability

Multiply the two independent probabilities: $P(X=2 \cap Y=\text{Blue}) = \frac{1}{4} \times \frac{1}{3}$

Answer:

B. $\frac{1}{12}$