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’.

Question

Philoid · Accepted Answer

The experiment is explained below in the tree diagram:

The sample space of the given experiment is:

Let E be the event that ‘the coin shows a tail’ and F be the event that ‘at least one die shows a 3’.

⇒ E = {1T, 2T, 4T, 5T} and F = {(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (6, 3)}

⇒ E ∩ F = ϕ ⇒ P(E ∩ F) = 0 ……….(i)

Now, we know that

By definition of conditional probability,

[Using (i)]

⇒ P(E|F) = 0