Answer to Question #202283 in Statistics and Probability for RAGHAV SOOD

Question

A,B and C are three events. Express the following events in set notations.

 (i) Simultaneous occurrence of A,B and C.

 (ii) Occurrence of at least one of them. 

 (iii) Both A and B occur and C does not occur. 

 (iv) The event B but not A occurs. 

 (v) Not more than one of the events A,B and C occur.

Answer 1

(i) Simultaneous occurrence of A,B and C

$A\cap B\cap C$

(ii) Occurrence of at least one of them. $A\cup B\cup C=(A^C\cap B^C\cap C^C)^C$

(iii) Both A and B occur and C does not occur. 

$A\cap B\cap C^C$

(iv) The event B but not A occurs. 

$B\cap A^C$

(v) Not more than one of the events A,B and C occur.$(A^C\cap B^C \cap C^C)\cup(A∩B^C∩C^C)$

$∪(A^C ∩B∩C ^C )∪(A^C∩B^C∩C)$