Question

A spinner is divided into 6 equal sectorslabeled 1-6. Grace spun the spinner threetimes. What is the probability that the sum ofher spins is less than 13 or greater than 15?

Answer 1

Solution

$Sample\text{ }Space=6^3=216$

To find the probability of less than 13 or greater than 15

$\begin{gathered} Possible\text{ outcome for 13}=(6,6,1),(6,5,2),(6,4,3),(5,5,3),(5,4,4) \\ Total\text{ Number of Outcomes}=3+3!+3!+3+3=21 \\ \\ Possible\text{ Outcome for 14}=(6,6,2),(6,5,3),(6,4,4),(5,5,4) \\ Total\text{ number of possible outcomes}=3+3!+3+3=15 \\ \\ Possible\text{ Outcome for 15}=(6,6,3),(6,5,4),(5,5,5) \\ Total\text{ number of possible outcomes}=3+3!+1=10 \\ \\ Overall\text{ Total}=21+15+10=46 \end{gathered}$

Therefore, the probability that the sum of her spins is less than 13 or greater than 15 is

$\begin{gathered} p=1-\frac{46}{216} \\ \\ p=\frac{170}{216} \\ \\ p=\frac{85}{108} \end{gathered}$