Given:
Let B and C be two events such that P (B) = 0.24 and P (C) = 0.33.
Required:
(a) Determine P (BUC), given that B and C are mutually exclusive.
(b) Determine P (BUC), given that B and C are independent.
Explanation:
The concept required:
a). For mutually exclusive events, the probability of both the events occurring at the same time is equal to zero.
[tex]\begin{gathered} P(B\cup C)=P(B)+P(C) \\ =0.24+0.33 \\ =0.57 \end{gathered}[/tex]
b).For independent events, the probability of both the events occurring at the same time is equal to non zero.
So,
[tex]\begin{gathered} P(B\cap C)=P(B)\times P(C) \\ =0.24\times0.33 \\ =0.0792 \end{gathered}[/tex]
and
[tex]\begin{gathered} P(B\cup C)=P(B)+P(C)-P(B\cap C) \\ =0.24+0.33-0.0792 \\ =0.4908 \end{gathered}[/tex]
Answer:
Determined the values of P (BUC) for both cases.