Answer:
The correct answer is 0.5.
Step-by-step explanation:
The probability of a spinner landing on the shaded part follows binomial distribution.
Equation to be used is P(r) = [tex]\left[\begin{array}{ccc}n\\r\end{array}\right][/tex] × [tex]p^{r}[/tex] × [tex]q^{n-r}[/tex] , where n is the number of times the spinner is spun and r is the number of times the spinner falls on the shaded region.
The probability of the spinner landing on the shaded part is p = [tex]\frac{1}{3}[/tex]. The probability of it landing on the unshaded part is q = [tex]\frac{2}{3}[/tex].
The spinner is spun n = 3 times.
We need to find the probability of it landing on the shaded part r = 2.
∴ Putting the values in the equation gives,
P(r) = [tex]\left[\begin{array}{ccc}3\\2\end{array}\right][/tex] × [tex]\frac{1}{2} ^{2}[/tex] × [tex]\frac{2}{3} ^{1}[/tex] = 3 × [tex]\frac{2}{3}[/tex] × [tex]\frac{1}{4}[/tex] = 0.5
