Given:
[tex]\begin{gathered} P\lparen C)\text{ = 0.69} \\ P\lparen C\text{ \mid A\rparen = 0.73} \\ P\lparen B)\text{ = 0.60} \\ P\lparen B\text{ \mid C\rparen = 0.77} \end{gathered}[/tex]
We are required to calculate:
[tex]P\lparen C\text{ or B\rparen}[/tex]
The events are non-mutually exclusive. Hence the probability of C or B can be calculated using the formula:
[tex]P\left(C\text{ or B}\right)\text{ = P\lparen C\rparen + P\lparen B\rparen - P\lparen C and B\rparen}[/tex]
and
[tex]P\lparen C\text{ and B\rparen = P\lparen C\rparen }\times\text{ P\lparen B \mid C\rparen}[/tex]
Substituting the given values:
[tex]\begin{gathered} P\lparen C\text{ or B\rparen = 0.69 + 0.60 - \lbrack0.69 }\times\text{ 0.77\rbrack} \\ =\text{ 0.7587} \end{gathered}[/tex]
Answer:
P(C or B) = 0.7587
