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 as three.

Explanation

A tree diagram is represented to show the outcomes of the given experiment.
sample space S of the experiment:
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 that event when coin shows tail and B be that event when at least one die gives 3.
So, A=(1,T)(2,T)(3,T)(4,T)
B={(3,1)(3,2)(3,3)(3,4)(3,5)(6,3)(3,6)}
since,`(AnnB)=phi`

hence, `P(AnnB)=0`

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