Question

helen spins two multicolored spinners. the probability that the first spinner lands on red is $\frac{4}{5}$. the probability that the second spinner lands on red is $\frac{7}{16}$. what is the probability that both spinners land on red? write your answer as a fraction or decimal. do not round.

Explanation:

Step1: Recall probability - multiplication rule

For independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\). The spins of the two spinners are independent events.

Step2: Identify the probabilities of each event

Let \(P(A)\) be the probability that the first spinner lands on red (\(P(A)=\frac{4}{5}\)) and \(P(B)\) be the probability that the second spinner lands on red (\(P(B)=\frac{7}{16}\)).

Step3: Calculate the probability that both spinners land on red

We use the multiplication - rule: \(P = P(A)\times P(B)=\frac{4}{5}\times\frac{7}{16}\).
\[

$$\begin{align*} \frac{4}{5}\times\frac{7}{16}&=\frac{4\times7}{5\times16}\\ &=\frac{28}{80}\\ &=\frac{7}{20}= 0.35 \end{align*}$$

\]

Answer:

\(\frac{7}{20}\) or \(0.35\)