NCERT Solutions
Class 12 Maths
Probability

Ex.13.1 Q.14
Consider the experiment of throwing a die, if a multiple of 3 comes up,
throw the die again and if any other number comes, toss a coin.
Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.
The outcomes of the given experiment can be represented by the following tree diagram. The sample space of the experiment is,
S = (1, H), (1, T), (2, H), (2, T), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, H), (4, T), (5, H), (5, T), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Let A be the event that the coin shows a tail and B be the event that at least one die shows 3.
So, A = {(1, t), (2, T), (4, t), (5, T)}
B = {(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (6, 3)}
=> A ∩ B = ф
=> P(A ∩ B) = 0
Then, P(B) = P{(3, 1)} + P{(3, 2)} + P{(3, 3)} + P{(3, 4)} + P{(3, 5)} + P{(3, 6)}
+ P{(6, 3)}
=
=
Probability of the event that the coin shows a tail, given that at least one die shows 3, is given by .
Therefore,