 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says Determine probability of E upon F when a coin is tossed three times where E is the event at least two heads and F is the event at most two heads So let's start the solution let S be the sample space of the experiment tossing a coin three times so the elements of S are that is S is equal to Htt That is head on the first toss and tails on the second and third toss similarly Htt That is heads on the first and second toss and tail on the third toss Htt that is heads on the three tosses again Htt H Ttt H Ttt Ttt and Ttt Now according to the question E is the event at least two heads and F is the event at most two heads So E is equal to That is elements of E are H H H H H H H H T H T H and T H H and F is equal to Htt H H T H H T H T T H T T H T T T T H T and T H H Now the elements common to E and F are that is E intersection F is equal to H H T H T H T H Now E has four elements and the sample space S has eight elements So the probability of E is equal to 4 upon 8 which is equal to 1 over 2 and the probability of F is 7 upon 8 and probability of E intersection F is equal to 3 upon 8 Now according to our key idea probability of E upon F is equal to probability of E intersection F upon probability of F So this is equal to 3 upon 8 into 8 upon 7 and this is equal to 3 upon 7 So the probability of E upon F is equal to 3 over 7 Hence the answer for this question is 3 upon 7 So this completes our solution I hope the solution is clear to you Bye and have a nice day