A point is selected at random from the interior of a circle. The probability that the point is closer to the centre than the boundary of the circle is

A point is selected at random from inside a circle. The probability that the point is closer to the circumference of the circle than to its centre, is

A point is selected at random from inside a circle. The probability that the point is closer to the circumference of the circle than to its centre, is

Name the points(s) On the boundary of the circle

There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9) Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle") =(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3) Now, answer the following questions. A point is selected at random inside a circle. The probability that the point is closer to the center of the circle than to its circumference is

There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9) Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle") =(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3) Now, answer the following questions. A point is selected at random inside a circle. The probability that the point is closer to the center of the circle than to its circumference is

A point is chosen at random inside a circle. Find the probability that the point is closer to the centre of the circle than to its circumference.

In the Fig. 13.12, J K L M is a square with sides of length 6 units. Points A and B are the mid-points of sides K L and L M respectively. If a point is selected at random from the interior of the square. What is the probability that the point will be chosen from the interior of J A B ? (FIGURE)

In the Fig.13.12,JKLM is a square with sides of length 6 units.Points A and B are the mid-points of sides KL and LM respectively. If a point is selected at random from the interior of the square.What is the probability that the point will be chosen from the interior of JAB?( FIGURE )