 Hello and welcome to the session. Let us discuss the following question. Question says, suppose you drop a dice at random on the rectangular region shown in figure 15.6. What is the probability that it will land inside the circle with diameter 1 meters? This is the given figure 15.6. First of all, let us understand that probability of occurrence of an event e denoted by Pe is defined as number of outcomes favourable to e upon total number of possible outcomes. Also, area of rectangle is equal to length multiplied by breadth. So we can write area of rectangle is equal to l into b where l is the length and b is the breadth. Also, area of circle is equal to pi r square where r is the radius of the circle. Now, we will use these expressions as our key idea to solve the given question. Let us now start with the solution. First of all, let us find out area of this given rectangle. We know length of rectangle that is l is equal to 3 meters and breadth of rectangle that is b is equal to 2 meters. Now, area of rectangle is equal to l into b that is length multiplied by breadth. Now, substituting corresponding values of l and b in this expression we get 3 multiplied by 2 meter square is equal to area of rectangle which is further equal to 6 meter square. So we get area of given rectangle is equal to 6 meter square. Now, we will find out area of this circle. We know diameter of this given circle is equal to 1 meters. Now, radius that is r is equal to 1 upon 2 meters. We know radius is equal to half of diameter. So, here r is equal to 1 upon 2 meters. Now, from key idea we know area of circle is equal to pi r square where r is the radius of the circle. Now, we will substitute 1 upon 2 for r in this expression and we get pi multiplied by square of 1 upon 2 meter square is equal to area of circle. Now, this is further equal to pi upon 4 meter square. Now, we have to find the probability that dice will land inside this circle. Now, we know dice can fall anywhere in this rectangular region. So, in this case total possible outcomes is equal to area of rectangular region which is further equal to 6 meter square. Now, favorable outcomes of dice to land inside this circle is equal to area of the circle. So, we can write total favorable outcomes of dice to land inside the circle is equal to area of circle which is further equal to pi upon 4 meter square. Now, from key idea we know probability of an event E is equal to number of outcomes favorable to E upon total number of possible outcomes. So, we get probability of dice to land inside the circle is equal to total area of the circle upon area of the rectangle. We know area of the circle is equal to pi upon 4 and area of the rectangle is equal to 6. Now, this is further equal to pi upon 24. Units of these two areas will get cancelled and we get probability of dice to land inside the circle is equal to pi upon 24. So, this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.