Find the
conditional probability of the event that ‘the die shows
a number greater than 4’ given that ‘there is at least
one tail’ Solution The outcomes of the experiment can be
represented in following diagrammatic manner called
the ‘tree diagram’ The sample space of the experiment may be
described as
S = {(H,H), (H,T), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
where (H, H) denotes that both the tosses result into
head and (T, i) denote the first toss result into a tail and
the number i appeared on the die for i = 1,2,3,4,5,6 Thus, the probabilities assigned to the 8 elementary
events
(H, H), (H, T), (T, 1), (T, 2), (T, 3) (T, 4), (T, 5), (T, 6)
are 1 1 1
1
1
1
1
1
,
,
,
,
,
,
,
4 4 12 12 12 12 12 12  respectively which  is
clear from the Fig 13