Question

helen spins two multicolored spinners.

• the probability that the first spinner lands on red is 4/5.
• the probability that the second spinner lands on red is 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: Use the multiplication rule for independent events

The multiplication rule for independent events states that if \(A\) and \(B\) are independent events, then \(P(A\cap B)=P(A)\times P(B)\). Let \(A\) be the event that the first spinner lands on red and \(P(A)=\frac{4}{5}\), and \(B\) be the event that the second spinner lands on red and \(P(B)=\frac{7}{16}\).

Step2: Calculate the probability

We want to find \(P(A\cap B)\). Using the formula \(P(A\cap B)=P(A)\times P(B)\), we substitute the values: \(P(A\cap B)=\frac{4}{5}\times\frac{7}{16}\).

Simplify the fraction: \(\frac{4\times7}{5\times16}=\frac{28}{80}=\frac{7}{20}\) (dividing numerator and denominator by 4).

Answer:

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