Mutually non-exclusive events are considered to be all those events that have the capacity to occur simultaneously in an experiment. The occurrence of one of them does not imply the non-occurrence of the other.
Unlike their logical counterpart, mutually exclusive events, the intersection between these elements is different from the void. This is:
P = 9/15
P = 9/15
P = 6/15
P = (9/15) + (9/15) - (6/15) = 12/15
When this result is multiplied by 100, the percentage of possibility that this event has is obtained.
(12/15) x 100% = 80%
2-For the second case, the groups are defined
A: {be citric} = {n1, n2, n3, n4, n5, n6, l1, l2, l3}
B: {be green} = {l1, l2, l3}
A ∩ B: {l1, l2, l3}
P = 9/15
P = 3/15
P = 3/15
P = (9/15) + (3/15) - (3/15) = 9/15
(9/15) x 100% = 60%
3-For the third case, proceed the same
A: {be fruit} = {n1, n2, n3, n4, n5, n6, l1, l2, l3, m1, m2, m3, s1, s2, s3}
B: {be green} = {l1, l2, l3}
A ∩ B: {l1, l2, l3}
P = 15/15
P = 3/15
P = 3/15
P = (15/15) + (3/15) - (3/15) = 15/15
(15/15) x 100% = 100%
In this case, the condition "Let it be fruit" includes the entire sample space, making the probability 1.
4- For the third case, proceed the same
A: {not citrus} = {m1, m2, m3, s1, s2, s3}
B: {be orange} = {n1, n2, n3, n4, n5, n6, m1, m2, m3}
A ∩ B: {m1, m2, m3}
P = 6/15
P = 9/15
P = 3/15
P = (6/15) + (9/15) - (3/15) = 12/15
(12/15) x 80% = 80%
References
- THE ROLE OF STATISTICAL METHODS IN COMPUTER SCIENCE AND BIOINFORMATICS. Irina Arhipova. Latvia University of Agriculture, Latvia.
- Statistics and the Evaluation of Evidence for Forensic Scientists. Second Edition. Colin GG Aitken. School of Mathematics. The University of Edinburgh, UK
- BASIC PROBABILITY THEORY, Robert B. Ash. Department of Mathematics. University of Illinois
- Elementary STATISTICS. Tenth Edition. Mario F. Triola. Boston St.
- Mathematics and Engineering in Computer Science. Christopher J. Van Wyk. Institute for Computer Sciences and Technology. National Bureau of Standards. Washington, DC 20234
- Mathematics for Computer Science. Eric Lehman. Google Inc.
F Thomson Leighton Department of Mathematics and the Computer Science and AI Laboratory, Massachussetts Institute of Technology; Akamai Technologies