Home
Class 12
MATHS
If P(A]B) > P(A), then which of the foll...

If P(A]B) > P(A), then which of the following is correct: (A) `P(B" "|" "A)" "<" "P(B)` (B) `P(AnnB)" "P(B)` (D) `P(B" "|" "A)" "=" "P(B)`

A

`P(B//A)ltP(B)`

B

`P(AnnB)ltP(A).P(B)`

C

`P(B//A)gtP(B)`

D

`P(B//A)=P(B)`

Text Solution

Verified by Experts

The correct Answer is:
A
(c)
Given
`P(A/B)gtP(A)implies(P(AnnB))/(P(B))gtP(A)`
`impliesP(AnnB)gtP(A).P(B)`
`implies(P(AnnB))/(P(A))gtP(B)impliesP(B/A)gtP(B)`
`[ :' P(B/A)=(P(AnnB))/(P(A))]`
Promotional Banner

Topper's Solved these Questions

  • PROBABIILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 13.5|15 Videos

  • MATRICES

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exerice|15 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If P(A|B) gt P(A) , then which of the following is correct:(A) P(B | A) lt; P(B) (B) P(AnnB) lt P(A)* P(B) (c) P(B|A) gt P(B) (D) P(B | A) = P(B)

If A and B are two events such that AsubB and P(B)!=0, them which of the following is correct? (A) P(A | B) =(P(B))/(P(A) (B) P(A|B)ltP(A) (C) P(A|B)geP(B) (D) none of these

Let A and B be two non-null events such that AsubeB . Then, which of the following statements is always correct? (1) (P(A/B)=P(B)−P(A) (2) P(A/B)>P(A) (3) P(A/B)≤P(A) (4) P(A/B)=1

If A and B are two independent events and P(A)=0.2, P(B)=0.3 , then find the values of the following: (i) P (A and B) (ii) P (A and not B) (iii) P (A or B) (iv) P (none of A and B)

P(A)=3//8; P(B)=1//2; P(AuuB)=5//8 , which of the following do/does hold good? a. P(A^c//B)=2P(A//B^c) b. P(B)=2P(A//B^c) c. 15 P(A^c//B^c)=8P(B//A^c) d. P(A^//B^c)=(AnnB)

If P(A/C) gt P(B/C) and P(A/(bar C)) gt P(B/(bar C)), then the relationship between P(A) and P(B) is (A) P(A)=P(B) (B) P(A) le P(B) (C) P(A) gt P(B) (D) P(A) ge P(B)

If A and B are any two events such that P(A) + P(B) - P(A a n d B) = P(A) ? then(A) P(B | A) = 1 (B) P(A | B) = 1 (C) P(B | A) = 0 (D) P(A | B) = 0

If A and B are two events, then which of the following does not represent the probability that exactly one of A ,B occurs is. (a) P(A) + P(B) - P(A nn B) (b) P(A nn B') + P(A' nn B) (c) P(A') + P(B') - 2P(A' nn B') (d) P(A) + P(B) -2 P(A nn B)

If P(A//B)=P(A//B ') , then prove that A and B are independent.

P is point in the interior of A B C as shown in fig.47.states which of the following statements are true (T) or false (F): A P+P B A C B P+P C=B C

NAGEEN PRAKASHAN ENGLISH-PROBABIILITY-Miscellaneous Exercise
  1. A and B are two events such that P(A)!=0. Find P(B|A) , if (i) A is a...

    Text Solution

    |

  2. A couple has two children. Find the probability that both the child...

    Text Solution

    |

  3. Suppose that 5% of men and 0.25% of women have grey hair. A grey haire...

    Text Solution

    |

  4. Suppose that 90% of people are right-handed. What is the probability t...

    Text Solution

    |

  5. An urn contains 25 balls of which 10 balls are red and the remaining g...

    Text Solution

    |

  6. In a hurdle race, a player has to cross 10 hurdles. The probability...

    Text Solution

    |

  7. A die is thrown again and again until three sixes are obtained. Fin...

    Text Solution

    |

  8. If a leap year is selected at random, what is the chance that it wi...

    Text Solution

    |

  9. An experiment succeeds twice as often as it fails. Then find the proba...

    Text Solution

    |

  10. How many times must a man toss a fair com so that the probability o...

    Text Solution

    |

  11. In a game, a man wins a rupee for a six and loses a rupee for any o...

    Text Solution

    |

  12. Suppose we have four boxes A,B,C and D containing coloured marbles ...

    Text Solution

    |

  13. Assume that the chances of a patient having a heart attack is 40%. ...

    Text Solution

    |

  14. If each element of a second order determinant is either zero or one, ...

    Text Solution

    |

  15. An electronic assembly consists of two sub-systems say A and B. From ...

    Text Solution

    |

  16. Bag 1 contains 3 red and 4 black balls and Bag II contains 4 red and 5...

    Text Solution

    |

  17. If A and B are two events euch that P(A) != 0 and P(B//A)=1 then

    Text Solution

    |

  18. If P(A]B) > P(A), then which of the following is correct: (A) P(B" ...

    Text Solution

    |

  19. If A and B are any two events such that P(A) + P(B) - P(A a n d B) = P...

    Text Solution

    |