Combined events: There are many times when two or more events occur together. Some common examples are:
(i) Tossing two coins together
There are four equally likely outcomes: {HH, HT, TH, TT}
(ii) Tossing three coins together
There are eight equally likely outcomes: {HHH, HTT, THH, TTH, HHT, HTH, THT, TTT}
Ex. P ( 3 heads or 3 tails) = \(\frac{1}{8}+\frac{1}{8}\) = \(\frac{2}{8}\)= \(\frac{1}{4}\)
(iii) Throwing two dice together
There are 36 equally likely outcomes:
{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,2), (6,3), (6,4), (6,5), (6,6)}
Ex. P ( a sum of 5) = \(\frac{4}{36}\) = \(\frac{1}{9}\)( \(\therefore\) There are four combinations to get a sum of 5. (1,4 ), (2,3), (3,2) and (4,1)).
