In an automated greenhouse, a monitoring system tracks high humidity levels (event HHH) and the activation of the mist irrigation system (event WWW). It is observed that:
P(H′∩W)=0.18andP(H′∩W′)=0.42 P(H' \cap W) = 0.18 \quad \text{and} \quad P(H' \cap W') = 0.42 P(H′∩W)=0.18andP(H′∩W′)=0.42Find P(H)P(H)P(H).
Find P(H∪W)P(H \cup W)P(H∪W).
Given that P(H∣W)=0.1P(H|W) = 0.1P(H∣W)=0.1,
find P(H∩W)P(H \cap W)P(H∩W).
Determine whether or not HHH and WWW are independent.
