 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says Determine probability of E upon F Two coins are tossed once where part one is I event tail appears on one coin and F is I event One coin shows hut in part two Is I event no tail appears and F is I event no hut appears Now we know that the conditional probability of the event E given that F has occurred that is 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 So this is a key idea behind that question We will use this formula to solve the above question So let's start the solution now according to the question two coins are tossed once so let S be the simple space of the experiment of tossing two coins once so S is equal to HT that is head on the first coin and tail on the second coin TH Tail on the first coin and F on the second coin HH and TT So S has four elements Now in part one it is given that E is the event that tail appears on one coin So obviously on the second coin there will be a hat so the elements of ER HT and F is the event that one coin shows hat if there is head on one coin Obviously there will be tail on the another coin So the elements of FR HT now E and F have the same elements. So E intersection F is equal to HT and TH now probability of E is equal to 2 upon 4 which is equal to 1 upon 2 and probability of F is also equal to 2 upon 4 which is equal to 1 upon 2 again the probability of E intersection F is equal to 2 upon 4 Which is equal to 1 upon 2 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 So this is equal to 1 upon 2 into 2 upon 1 Which is equal to 1 Hence the answer for this part is 1 now in part 2 we are given E is the event no tail appears on any coin and F is the event that no head appears on any coin So obviously E has only one element which is HH and and F also has only one element which is TT So E intersection F is equal to 5 now probability of E is equal to 1 upon 4 and probability of F is also 1 upon 4 But probability of E intersection F is equal to 0 So according to our key idea we have probability of E upon F is equal to probability of E intersection F Which is 0 upon probability of F which is 1 over 4 and This is again equal to 0 Hence the answer for this part is 0 So this completes our session. I hope the solution is clear to you. Bye and have a nice day