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A point is chosen at random inside a cir...

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.

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The correct Answer is:
`therefore P(A) = (n(A))/(n(S))= ((pir^(2))/4)/(pir^(2))=(pir^(2))/4xx1/(pir^(2))=1/4`
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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

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There are two circles in the x-y plane whose equations are x^2+ y^2 - 2y = 0 and x^2 + y^2- 2y - 3 = 0 . A point is chosen at random inside the larger circle. Find the probability that the point has been taken from outside the smaller circle.

There is a point inside a circle. What is the probability that this point is close to the circumference than to the centre ?

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

MARVEL PUBLICATION-PROBABILITY-MULTIPLE CHOICE QUESTIONS
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  2. Set of all possible outcomes of an experiment is called its

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  3. If S is the sample space of an experiment, than S must contain

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  4. If S(1),S(2) are the sample spaces of an experiment at the first two t...

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  5. If A an event in a sample space S, then

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  6. If P(A) denotes the probability of an event, then

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  7. Which of the following subsets of a sample space S represents an impos...

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  8. Probability of an impossible event

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  9. Which of the following subsets of a sample space S represents a certai...

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  10. The probability of a certain event is 0 (b) 1 (c) greater than 1...

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  11. A coin is tossed once. Write its sample space.

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  12. If one coin is tossed twice (or two coins tossed once), then the sampl...

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  13. If a coin is tossed three times (or three coins are tossed together...

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  14. If one coin is tossed n times (or n coins tossed once), then the numbe...

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  15. If one die is rolled once, then the sample space is

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  16. If one die is rolled n times (or n dice rolled once), then the number ...

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  17. If s is the total score when two dice are thrown once then

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  18. Indicate the probability of the following events an even number, in ...

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  19. If one die is rolled then find the probability of each of the followin...

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  20. Indicate the probability of the following events a prime number, in ...

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  21. Indicate the probability of the following events a number which is b...

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