Question

if the pointer in the figure is spun twice, find the probability that the pointer lands on green and then red.
the probability is
(type a fraction. simplify your answer.)

Explanation:

Step1: Calculate the probability of landing on green

The spinner is divided into 4 equal - sized sections. Let's assume the green section is 1 out of 4. So the probability of landing on green \(P(G)=\frac{1}{4}\).

Step2: Calculate the probability of landing on red

Since the spinner is spun again (independent event), and the red section is also 1 out of 4. So the probability of landing on red \(P(R)=\frac{1}{4}\).

Step3: Use the multiplication rule for independent events

For two independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\). Here \(A\) is the event of landing on green and \(B\) is the event of landing on red. So \(P(G\cap R)=P(G)\times P(R)\). Substitute \(P(G)=\frac{1}{4}\) and \(P(R)=\frac{1}{4}\) into the formula: \(P(G\cap R)=\frac{1}{4}\times\frac{1}{4}\).

Answer:

\(\frac{1}{16}\)