InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
For three events `A ,B`and `C ,P`(Exactly one of `A`or `B`occurs) `=P`(Exactly one of `B`or `C`occurs) `=P`(Exactly one of `C`or `A`occurs) `=1/4`and `P`(All the three events occur simultaneously) `=1/6dot`Then the probability that at least one of theevents occurs, is :`7/(64)`(2) `3/(16)`(3) `7/(32)`(4)`7/(16)`A. `(3p+2p^(2))/(2)`B. `(p+3 p^(2))/(2)`C. `(3 p+ p^(2))/(2)`D. `(3 p +2 p^(2))/(4)` |
|
Answer» Correct Answer - A We have, `P(A)+P(B)-2P(A cap B)=P` `P(B)+P(C )-2P(B cap C)=p` `P(C )+P(A)-2P(C cap A)=p` and, `P(A cap B cap C)=p^(2)` Adding (i),(ii) and (iii), we get `2[P(A)+P(B)+P(C )+P(A cap B)-P(B cap C)-P(A cap C)]=3p` `implies P(A)+P(B)+P(C )-P(A cap B)-P(B cap C)` `P(A cap C)=3p//2` `therefore` Required probability `=P(A cup B cup C)` `=P(A)+P(B)+P(C )-P(A cap B)-P(B cap C)-P(A cap C)+P(A cap B cap C)` `=(3p)/(2)+p^(2)=(3p+2p^(2))/(2)` |
|