 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 head on third toss and F is the event Heads on first two tosses Now we know that if E and F are two events associated with the same sample space of a random experiment the conditional probability of the event E given that F has occurred that is probability of E upon F is given by 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 the key idea behind our question We will take the help of this key idea to solve the above question So let's start the solution Let S be the sample space of the experiment of tossing a coin three times therefore S is equal to T T that is head on the first toss and tails on the second and third toss H T that is head on the first and second toss and tail on the third toss H H H that is all the tosses result into head again H T H T T H T T T that is tail on all the three tosses T H T T H H So S has eight elements Now according to the question E is the event that head on third toss and F is the event heads on first two tosses So E is equal to head on third toss that is H H H H T H T T H and T H H and F is equal to H H T H H So E intersection F is equal to H H H only Now probability of E is equal to 4 upon 8 which is equal to 1 over 2 and probability of F is equal to 2 upon 8 which is equal to 1 upon 4 and probability of E intersection F is equal to 1 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 and this is equal to 1 upon 8 into 4 upon 1 which is equal to 1 over 2 Hence the answer for this question is 1 upon 2 I hope the solution is clear to you Bye and take care