Answer
First Part
P (Spinning Purple and getting a Green Star)
= P (Spinning Purple) × P (getting a Green Star)
= (1/4) × (1/5)
= (1/20)
Second Part
P (Spinning Blue or getting a Black Triangle)
= P (Spinning Purple) + P (getting a Green Star)
= (3/8) + (2/5)
= (15/40) + (16/40)
= (31/40)
Step-by-step explanation
The probability of an event is calculated as the number of elements in the event divided by the total number of elements in the sample space.
And combined probability for two events that do not depend on each other (independent events) is the product of the respective probabilities of the two events.
But when or is used to combine the probabilities, it is usually a sum of probabilities of the respective events.
First Part
P (Spinning Purple and getting a Green Star)
= P (Spinning Purple) × P (getting a Green Star)
P (Spinning Purple)
Number of spaces coloured Purple = n {1, 8} = 2
Total number of spaces = n {1, 2, 3, 4, 5, 6, 7, 8} = 8
P (Spinning Purple) = (2/8) = ¼
P (getting a Green Star)
Number of Green Stars = 1
Total Number of figures = 5
P (getting a Green Star) = (1/5)
P (Spinning Purple and getting a Green Star)
= P (Spinning Purple) × P (getting a Green Star)
= (1/4) × (1/5)
= (1/20)
Second Part
P (Spinning Blue or getting a Black Triangle)
= P (Spinning Purple) + P (getting a Green Star)
P (Spinning Blue)
Number of spaces coloured Blue = n {4, 5, 6} = 3
Total number of spaces = n {1, 2, 3, 4, 5, 6, 7, 8} = 8
P (Spinning Blue) = (3/8)
P (getting a Black Triangle)
Number of Black Triangles = 2
Total Number of figures = 5
P (getting a Black Triangle) = (2/5)
P (Spinning Blue or getting a Black Triangle)
= P (Spinning Purple) + P (getting a Green Star)
= (3/8) + (2/5)
= (15/40) + (16/40)
= (31/40)
Hope this Helps!!!