Find p[b] in each case: (a) events a and b are a partition and p[a] = 3p[b]. (b) for events a and b, p[a ∪ b] = p[a] and p[a ∩ b] = 0. (c) for events a and b, p[a ∪ b] = p[a]− p[b].

Case(a):

Case(b):

Case(c):  

Step-by-step explanation:

Given

(a) events a and b are a partition and p[a] = 3p[b].

(b) for events a and b, p[a ∪ b] = p[a] and p[a ∩ b] = 0.

(c) for events a and b, p[a ∪ b] = p[a]− p[b].

we have to find the p[b] in each case:

Case (a): events a and b are a partition and p[a] = 3p[b].

gives

Case (b):  for events a and b, p[a ∪ b] = p[a] and p[a ∩ b] = 0.

⇒ ⇒  ∵  p[a ∩ b] = 0.

Case(3):  for events a and b, p[a ∪ b] = p[a]− p[b].

p[a ∪ b] = p[a]− p[b]

⇒

⇒

⇒  

answer: answer

step-by-step explanation: