An unfair spinner has yellow, green and blue sections. The Probability of landing on either yellow or blue is 0.6. The probability of landing on either yellow or green is 0.8.
What is the probability of the following?
a) landing on green=..............................................................
b) landing on blue=................................................................
c) landing on yellow=.............................................................
d) landing on blue or green=..................................................
+130536 P ( Y or B) = P(Y) + P(B) - P (Y and B) → 0.6 = P(Y) + P(B) - 0 (1)
P ( Y or G) = P(Y) + P(G) - P (Y and G) → 0.8 = P(Y) + P(G) - 0 (2)
P(Y) + P(B) + P(G) = 1 (3)
Add (1) and (2), and we have
1.4 = 2P(Y) + P(B) + P(G) → 1.4 - 2P(Y) = P(B) + P(G) (4)
Subbing (4) into (3), we have
P(Y) + 1.4 - 2P(Y) = 1 simplify
-P(Y) = -0.4 → P(Y) = 0.4
So using (1)
0.6 = 0.4 + P(B) - 0 → P(B) = 0.2
And using (2)
0.8 = 0.4 + P(G) - 0 → P(G) = 0.4
And the probability of landing on blue or green =
P(B or G) = P(B) + P(G) - 0 = 0.2 + .0.4 = 0.6
