Home
Class 12
MATHS
If A,B,C are three events in a random ex...

If A,B,C are three events in a random experiment, Prove the following.
`P((A)/(A))=1`

Text Solution

Verified by Experts

The correct Answer is:
`=1`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise DAM SURE|13 Videos

  • PROBABILITY

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE-9(b)|24 Videos

  • PERMUTATIONS AND COMBINATIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TAXTUAL EXERCISES|73 Videos

  • QUADRATIC EXPRESSIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES|68 Videos

Similar Questions

Explore conceptually related problems

If A,B,C are three events in a random experiment, Prove the following. P((phi)/(A))=0

If A,B,C are three events in a random experiment, Prove the following. P(A-B)=P(A)-P(AcapB)

If A,B,C are three events in a random experiment, Prove the following. AsubeBrArrP((A)/(C))leP((B)/(C))

If A, B, C are three events associated with a random experiment, prove that P(A uu B uu C) = P(A) + P(B) + P(C) - P(A nn B) - P(A nn C) P(B nn C) + P (A nn B nn C)

If A, B, C are any three events in an experiment then show that (i) P(A//B^(C)) = (P(A) - P(A nn B))/(1-P(B)) "if P"(B^(C)) gt 0 (ii) A sube B rArr P(A//C) le P(B//C) "if P(C)" gt 0 (iii) If A, B are mutually exclusive, then P(A//B^(C)) = (P(A))/(1-P(B)) "if P(B)" ne 1 (iv) If A, B are mutually exclusive and P(A uu B) ne 0 "then" P(A//A uu B) = (P(A))/(P(A) + P(B))

Let E, overlineE , be the complimentary events, in a random experiment , then which of the following is true?

(i) If A,B,C are any three events in an experiment and AsubeB , P(C ) gt 0 then show that P(A//C) le P(B//C) (ii) If A, B are mutually exclusive and P(B) ne 1 then show that P(A//B^(C ))=(P(A))/(1-P(B)) (iii) If A, B are mutually exclusive and P(AuuB) ne 0 then P(A//AuuB)=(P(A))/(P(A)+P(B))

If A and B are any two events of a random experiment then show that (i) P(A^(C) nn B^(C)) = P(A^(C)) - P(B) "if A" nn B = phi (ii) P(A^(C)//B^(C)) = (1-P(A uu B))/(1-P(B)) "with P(A)" ne 0 and P(B) ne 1

If A and B are two independent events of a random experiment such that P(A capB) = (1)/(6) and P(overlineA cap overline B) = (1)/(3) , then P(A)=

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-PROBABILITY-Exercise -9 ( c)
  1. A and B are two independent events such that the probability of the bo...

    Text Solution

    |

  2. A fair die is rolled. Consider the events. A={1,3,5},B={2,3} and C =...

    Text Solution

    |

  3. If A,B,C are three events in a random experiment, Prove the following....

    Text Solution

    |

  4. If A,B,C are three events in a random experiment, Prove the following....

    Text Solution

    |

  5. If A,B,C are three events in a random experiment, Prove the following....

    Text Solution

    |

  6. If A,B,C are three events in a random experiment, Prove the following....

    Text Solution

    |

  7. If A,B are mutually exclusive and P(B)gt0 " then "P((A)/(B))=0.

    Text Solution

    |

  8. If A,B, are ,mutually exclusive then P(A//B^(C))=(p(A))/(1-P(B))," w...

    Text Solution

    |

  9. If A,B are mutually exclusive and P(AcupB)ne0 then p((A)/(AcupB))=(P...

    Text Solution

    |

  10. Suppose that a coin is tossed three times. Let A be "getting three hea...

    Text Solution

    |

  11. Suppose that an unbaised pair of dice is rolled. Let A denote the even...

    Text Solution

    |

  12. Prove that A and B are independent events if and only if P((A)/(B))=P(...

    Text Solution

    |

  13. Suppose A and B are independent events with P(A)=0.6, P(B)=0.7 then co...

    Text Solution

    |

  14. The probability that Australia wins a match against India in a cricket...

    Text Solution

    |

  15. A person secures a job in a construction company in which the probabi...

    Text Solution

    |

  16. For any two events A,B shows that P(AcapB)-P(A)P(B)=P(A^(C))P(B)-P(A...

    Text Solution

    |

  17. Three Urns have the following composition of balls. Urn I : 1 white,...

    Text Solution

    |

  18. In a shooting test the probability of A,B,C hitting the targets are (1...

    Text Solution

    |

  19. In a certain college, 25% of the boys and 10% of the girls are studyin...

    Text Solution

    |

  20. 4 A person is known to speak truth 2 out of 3 times. He throws a die a...

    Text Solution

    |