The spins are independent from each other. So, if we want three consecutive specific results, the probability of the three results occuring consecutively will be the product of the probability of each resukt.
The results we want are: green then blue then purple.
The spinner has 8 equal regions, 2 of them are green, 3 of them are blue and 1 of them is purple.
The probability of landing on green is the number of green regions (the result we want) divided by the total number of regions (all the possible results).
For, for the first spin, we have:
[tex]\frac{2}{8}=\frac{1}{4}[/tex]For the second spin, we want blue, and we have 3 regions, so the probability is:
[tex]\frac{3}{8}[/tex]And the final spin we want purple, and we have only one purple, so the probability is:
[tex]\frac{1}{8}[/tex]So, the final probability will be:
[tex]\frac{1}{4}\cdot\frac{3}{8}\cdot\frac{1}{8}=\frac{3}{256}[/tex]So, the final probability is 3/256.
