 Hello and welcome to the session. In this session we will discuss a question which says that each of the given statements describe two events are these two events dependent or independent? First statement is given as you randomly draw a marble from a bag containing 7 red marbles and 11 green marbles you put the marble back and then draw a second marble and the second statement is John rolls a six-sided die and gets number three at the same time and he spins a spinner and gets a blue color and the next statement is Mary asks a classmate to be her partner for a class project and she agrees to work with her. Next, her friend Alice picks a partner too. Now let us start with the solution of the given question. First of all, let us start with the A part. In the first part it is given that a bag contains 7 red marbles and 11 green marbles Now in total there are 18 marbles that is 7 red marbles plus 11 green marbles. Now if a marble is drawn at random then there will be 17 marbles and this marble is put back in the bag then again there will be 18 marbles. So here the number of marbles remains same. Now again from these 18 marbles the second marble will be drawn at random. So here the first drawn marble does not have any effect on the second drawn marble as both of these marbles are drawn at random from a bag containing 18 marbles. So both these events are independent. Now let us start with the B part. Now in the B part it is given that John rolls a die and Andrew spins a spinner. Now another drawn in rolling a die has nothing to do with spinning a spinner. This means both events are independent. Now let us discuss the C part. Now in the C part let us take a class of 10 students. Now it is given that Mary asks a classmate to be her partner for a class project. This means Mary selects a partner from this class and also it is given that after Mary selection her friend Alice picks a partner too. So now after Mary selection there is a change in the total strength of the class because person selected by Mary cannot be the partner of Alice. Now Alice selects a partner from a class of 9 students. Now from here you can see that Mary selects a partner from a class of 10 students and then after Mary selection Alice selects a partner from a class of 9 students. So Mary selection has an effect on Alice selection of partner therefore the two events are dependent. This is the solution of the given question. That's all for this session. Hope you all have enjoyed the session.