Can two events be mutually exclusive and independent simultaneously?

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible.
\(P(A)=\frac { 4 }{ 7 } ,P(B)=\frac { 1 }{ 7 } ,P(C)=\frac { 2 }{ 7 } \)

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
\(P(A)=\frac { 2 }{ 5 } ,\quad P(B)=\frac { 1 }{ 5 } ,\quad P(C)=\frac { 3 }{ 5 } \)

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible.
\(P(A)=0.3,P(B)=0.9,P(C)=-0.2\)

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible.
\(P(A)=\frac { 1 }{ \sqrt { 3 } } ,\quad P(B)-1-\frac { 1 }{ \sqrt { 3 } } ,\quad P(C)-0\)

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible.
P(A) = 0.421, P(B) = 0.527  P(C) = 0.042

When a pair of fair dice is rolled, what are the probabilities of getting the sum (i)7 (ii) 7 or 9 (iii) 7 or 12?

If A and B are mutually exclusive events P(A) = \(\frac{3}{8}\) and P(B) = \(\frac{1}{8}\) , then find (i) P(\(\bar { A } \)) (ii) \(P(A\cup B)\) (iii) \(P(\bar { A } \cap B)\) (iv) \(P(\bar { A } \cup \bar { B } )\)

If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15. Find (i) P(only B) (ii) \(P(\bar{B})\) (iii) P(only A)

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of
(i) \(P(A\cup B)\) (ii) \(P(A\cap \bar { B } )\) (iii) \(P(\bar { A } \cap B)\)