91影视

When two events have no components (their intersection is the empty set), they are said to be mutually exclusive. Therefore, $\mathbf{\text{P (A}}\mathbf{鈭�}\mathbf{\text{B) = 0}}$. It signifies that the chances of events A and B occurring are nil.

Since A and B are mutually exclusive.

Therefore,

$\mathbf{\text{P (A}}\mathbf{鈭�}\mathbf{\text{B) = 0}}$

By addition theorem on probability:

$\begin{array}{c}\mathbf{\text{P(A}}\mathbf{鈭�}\mathbf{\text{B) = P(A) + P(B)}}\mathbf{鈭�}\mathbf{\text{P(A}}\mathbf{鈭�}\mathbf{\text{B)}}\\ \mathbf{\text{= 0.30 + 0.55}}\mathbf{鈭�}\mathbf{\text{0}}\\ \mathbf{\text{= 0.85}}\end{array}$

Hence, the required probability is 0.85.

Since A and C are mutually exclusive.

Therefore,

$\mathbf{\text{P (A}}\mathbf{鈭�}\mathbf{\text{C) = 0}}$

Hence, the required probability is 0.

$\begin{array}{c}\mathbf{\text{P (A/B)=}}\frac{\mathbf{\text{P (A}}\mathbf{鈭�}\mathbf{\text{B)}}}{\mathbf{\text{P (B)}}}\\ \mathbf{\text{=0}}\end{array}$

Hence, the required probability is 0.

$\begin{array}{c}\mathbf{\text{P (B}}\mathbf{鈭�}\mathbf{\text{C) = P (B) + P (C)}}\mathbf{鈭�}\mathbf{\text{P (B}}\mathbf{鈭�}\mathbf{\text{C)}}\\ \mathbf{\text{= 0.55 + 0.15}}\mathbf{鈭�}\mathbf{\text{0}}\\ \mathbf{\text{= 0.70}}\end{array}$

Hence, the required probability is 0.70.

Yes, the occurrences are independent because the occurrence of one guarantees that the others will not occur. As a result, B and C are independent.