24 votes 24 votes Let $A, B,$ and $C$ be independent events which occur with probabilities $0.8, 0.5,$ and $0.3$ respectively. The probability of occurrence of at least one of the event is _______ Probability gate1994 probability normal numerical-answers independent-events + – Kathleen asked Oct 4, 2014 edited Jan 12, 2023 by shadymademe Kathleen 4.4k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 34 votes 34 votes $P(A) = 0.8 \implies P(A') = 1 - 0.8 = 0.2$ $P(B) = 0.5 \implies P(B') = 1 - 0.5 = 0.5$ $P(C) = 0.3 \implies P(C') = 1 - 0.3 = 0.7$ $P$ (No event will occur)$ = 0.2 \ast 0.5 \ast 0.7 = 0.07$ $P$ (at least $1$ event will occur)$ = 1 - 0.07 = 0 .93$ Manu Thakur answered Oct 10, 2014 edited Apr 23, 2021 by Lakshman Bhaiya Manu Thakur comment Share Follow See all 2 Comments See all 2 2 Comments reply srestha commented May 17, 2019 reply Follow Share or We can calculate like this $0.8\times 0.5\times 0.7+0.2\times 0.5\times 0.7+0.2\times 0.5\times 0.3+0.8\times 0.3\times 0.5+0.8\times 0.5\times 0.7+0.5\times 0.3\times 0.2+0.8\times 0.3\times 0.5=0.93$ Inclusion-Exclusion principle is not working here 1 votes 1 votes shashankrustagi commented Dec 5, 2020 reply Follow Share Take 7 of the 8 cases here. 0 votes 0 votes Please log in or register to add a comment.
7 votes 7 votes P(at least A or B or C )= P(A u B u c) = 0.8+0.5+0.3-(0.8*0.5) -(0.5 *0.3) -(0.8*0.3)+(0.8*0.5*0.3) =1.6-0.67 =0.93 sutanay3 answered Jun 14, 2018 sutanay3 comment Share Follow See all 4 Comments See all 4 4 Comments reply vishalshrm539 commented Jan 1, 2019 reply Follow Share This is right but above method is fast. 0 votes 0 votes Amcodes commented Oct 8, 2020 reply Follow Share Aren’t you calculating EXACTLY one? because either A or B or C any one occurs in your case and not (A and B) , (A and C) etc? 0 votes 0 votes neel19 commented Jan 2, 2021 reply Follow Share I have the same doubt. Does at least one mean “only one but not both or all three together”? 0 votes 0 votes Amcodes commented Jan 3, 2021 reply Follow Share @neel19 (A U B U C) exactly works as OR gate , OR gate returns true only if atleast one of inputs is true. 0 votes 0 votes Please log in or register to add a comment.