Question

a. Given P(K) = 0.45, P(L ) = 0.27, and P(K L) = 0.13. Draw a Venn diagram, fill in the probabilities, and determine the following: 

i. P (K  L)

ii. P (K  L’)

iii. P (K’  L’)

Answer 1

Part i)

$P(K \bigcup L) = P(K)+P(L)-P(K \bigcap L)$

$$0.45+0.27-0.13=0.59$$

Part ii)

$$P(K \bigcap L') = P(K) - P(K \bigcap L)$$ $$0.45-0.13=0.32$$

Part iii)

$$P(K' \bigcap L') = 1-P(K \bigcup L)$$ $$1-0.59=0.41$$

Venn diagrams