Consider an experiment of tossing a coin.If the coin shows heads,toss it again but if it shows tails,then throw a die.Find the conditional probability of event that 'the die shows a number greater than 4' given that 'there is atleast one tail'.

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 probability assigned to the 8 elementary events.
(H,H) ,(H,T ) (T,1),(T, 2), (T, 3) (T, 4), (T, 5), (T, 6)
are 1/4,1/4,1/12,1/12,1/12,1/12,1/12,1/12 respectively


Let F be the event that ‘there is at least one tail’ and E be the event ‘the die shows
a number greater than 4’. Then
F = {(H,T), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
E = {(T,5), (T,6)} and E ∩ F = {(T,5), (T,6)}
Now P(F) = P({(H,T)}) + P ({(T,1)}) + P ({(T,2)}) + P ({(T,3)})
+ P ({(T,4)}) + P({(T,5)}) + P({(T,6)})
= 1/4 ,+ 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 = 3/4
And P(E ∩ F) = P ({(T,5)}) + P ({(T,6)}) = 1/12 +1/12 = 1/6