Question

a spinner is divided into sections that are both colored and numbered. the event that the spinner lands on a green section is independent from the event that it lands on an odd - numbered section. which of the following sets of probabilities could be associated with this spinner?

p(green) = 0.25
p(odd) = 0.2
p(green and odd) = 0.45

p(green) = 0.12
p(odd) = 0.2
p(green and odd) = 0.06

p(green) = 0.18
p(odd) = 0.2
p(green and odd) = 0.036

p(green) = 0.24
p(odd) = 0.2
p(green and odd) = 0.012

Explanation:

Step1: Recall the formula for independent events

If two events \(A\) and \(B\) are independent, then \(P(A\cap B)=P(A)\times P(B)\)

Step2: Check each option

• Option 1:

\(P(\text{green})\times P(\text{odd})=0.25\times0.2 = 0.05
eq0.45\)

• Option 2:

\(P(\text{green})\times P(\text{odd})=0.12\times0.2=0.024
eq0.06\)

• Option 3:

\(P(\text{green})\times P(\text{odd})=0.18\times0.2 = 0.036\)

• Option 4:

\(P(\text{green})\times P(\text{odd})=0.24\times0.2=0.048
eq0.012\)

Answer:

The set of probabilities \(P(\text{green}) = 0.18\), \(P(\text{odd})=0.2\), \(P(\text{green and odd}) = 0.036\) could be associated with the spinner.