Question

the arrows on two spinners are spun one time. the first spinner is divided equally into the numbers 1, 2, 3, and 4. the second spinner is divided equally into the colors red, blue, green, and yellow. all possible outcomes are shown in the table. what is the probability that the first spinner lands on red or the second spinner lands on an even number?
a. $\frac{1}{8}$
b. $\frac{1}{4}$
c. $\frac{5}{8}$
d. $\frac{3}{4}$
e. $\frac{7}{8}$

Explanation:

Step1: Calculate probability of first spinner landing on red

The first spinner has 4 colors. The probability of landing on red, $P(R)$, is $\frac{1}{4}$ since there is 1 red - color out of 4 colors.

Step2: Calculate probability of second spinner landing on an even number

The second spinner has 4 numbers (1, 2, 3, 4). The even - numbered outcomes are 2 and 4. So the probability of landing on an even number, $P(E)$, is $\frac{2}{4}=\frac{1}{2}$.

Step3: Calculate probability of both events happening

The probability of the first spinner landing on red and the second spinner landing on an even number, $P(R\cap E)$. There are 2 cases where this happens: (R, 2) and (R, 4). So $P(R\cap E)=\frac{2}{16}=\frac{1}{8}$.

Step4: Use the addition rule of probability

The addition rule of probability for two events $A$ and $B$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event that the first spinner lands on red and $B$ is the event that the second spinner lands on an even number. So $P(R\cup E)=P(R)+P(E)-P(R\cap E)=\frac{1}{4}+\frac{1}{2}-\frac{1}{8}=\frac{2 + 4-1}{8}=\frac{5}{8}$.

Answer:

C. $\frac{5}{8}$