Question

If you have a spinning wheel with $3$ green sectors, $1$ blue sector, and $1$ red sector, what is the probability of getting a green sector? What is the probability of getting a non-blue sector?

Answer 1

Step 1: Calculate the total number of sectors

It is given that the number of

Green sector $g=3$

Blue sector $b=1$

Red sector $r=1$

Hence the total number of sectors in the spinning wheel,

$t=g+b+r$

$=3+1+1$

$=5$ sectors

Step 2: Calculate the probability of green sectors

Probability of green sector,

$P\left(g\right)=\frac{g}{t}$ [Probability $=\frac{\mathrm{Number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$]

$=\frac{3}{5}$

Step 3: Calculate the probability of non-blue sectors

Total number of non-blue sector

$t_b=g+r$

$=3+1$

$=4$

Therefore, the probability of non-blue sector

$P\left(t_b\right)=\frac{t_b}{t}$ [Probability $=\frac{\mathrm{Number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$]

$=\frac{4}{5}$

Hence, the required probabilities are $\frac{3}{5}$ and $\frac{4}{5}$.