 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says Consider the experiment of throwing a dime if a multiple of three 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 three So let's start the solution Now we have to consider the experiment of throwing a die in which if a multiple of three comes up We have to throw the die again and if any other number comes up Then we have to toss a coin now the outcomes of the Experiment can be represented in our diagrammatic manner called the pre diagram So here when we throw a die any number from one to six can appear So if a multiple of three comes up that is either three or six comes up Then again we have to throw a die But if any other number comes up that is if One two and four and five comes up then we have to toss a coin So from this three diagram the sample space experiment May be described as is equal to One h one t three one three two three three four three five three six four h forty five h five t six one six two six three six four six five and six six therefore the sample space s has 20 elements now we have to find the Conditional probability of the event the coin shows a tail given that at least one die shows a three so let E be the event that the event one die shows a three consisting of elements one t two t Four t five t and f is a set consisting of elements Three one three two three three three four three five three six three now Here we observe that e intersection f is equal to five Therefore probability of e Intersection f is equal to zero now according to our key idea we have probability of e upon f is equal to probability of e intersection f upon probability of f Provided probability of f is not equal to zero since probability of e intersection f is equal to zero this implies probability of e upon f is equal to zero Hence the conditional probability of the event the coin shows a tail given that at least one die shows a three is zero So the answer for the above question is zero This completes our session. I hope the solution is clear to you. Bye and have a nice day