Home
Class 12
MATHS
For any events A and B. Given P(AuuB)=0....

For any events `A` and `B`. Given `P(AuuB)=0.6`, `P(A)=P(B)=0.4`, Then the value of `P[AnnB]` is

A

`1//3`

B

`1//2`

C

`1//4`

D

`1//5`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Let `P(A)=P(B)=p` (say)
`P(B//A)=(P(BnnA))/(P(A))`
`:.(0.8)p=P(BnnA)`………..`(i)`
`P(AuuB)=p+p-P(AnnB)`
`0.6=2p-p(0.8)=(1.2)p`
`:.p=(0.6)/(1.2)=(1)/(2)`
`:.P(A)=P(B)=(1)/(2)`
Now, `P[AnnbarB) uu (barAnnB)]`
`=P(A)+P(B)-2P(AnnB)`
`=1-2(0.8)(1)/(2)=0.2=(1)/(5)`
Promotional Banner

Topper's Solved these Questions

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE PUBLICATION|Exercise Sovled Examples|22 Videos

  • PROBABILITY I

    CENGAGE PUBLICATION|Exercise JEE Advanced|7 Videos

Similar Questions

Explore conceptually related problems

For any two events A and B prove that, P(A cup B) le P(A) + P(B)

If P(A) = 3/7,P(B)=4/7,P(AnnB)=2/9 then the value of P(A//B) is

If for independent events A and B, P(A) = 0.3, P(B) = 0.6, then what will be the value of P(A nn B) ?

Given 2 mutually exclusive events A and B such that P(A) = 0.45, P(B) = 0.35. Then the value of P(A nn B) wqill be

For any two events A and B prove that P(A cup B) le P{A) + P (B) .

If P(A)=0.54, P(B)=0.69 and P(A cap B)=0.35 , then the value of P(A' cup B') is-

If P(A cup B)=0.8 and P(A cap B)=0.3 then the value of [P(barA)+P(barB)] is -

For any two events A and B, show that, P(A uu B) = P(A) + P(B) - P(A nn B) .

If A and B are two events such that P(AnnB)=0.3 and P(A'nnB')=0.6 , then the value of P(A)+P(B) is equal to

If two events A and B are such as P(A^(c ))=0.3, P(B)=0.4 and P(A cap B^(c ))=0.5 , find the value of P[B//(A cup B^(c ))] .

CENGAGE PUBLICATION-PROBABILITY-All Questions
  1. A bag contains four tickets marked with numbers 112,121,211, and 222. ...

    Text Solution

    |

  2. For two events A and B, if P(A)=P((A)/(B))=(1)/(4) and P((B)/(A))=(1)/...

    Text Solution

    |

  3. A and B are events of an experiment such that 0 lt P(A), P(B) lt 1. If...

    Text Solution

    |

  4. If A and B are two events such that P(A)=0.3, P(B)=0.25, P(AnnB)=0.2, ...

    Text Solution

    |

  5. A number is selected at random from the first 25 natural numbers. I...

    Text Solution

    |

  6. If two events A and B such that P(A')=0.3, P(B)=0.5 and P(AnnB)=0.3, t...

    Text Solution

    |

  7. In a hurdle race, a runner has probability p of jumping over a specifi...

    Text Solution

    |

  8. Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5...

    Text Solution

    |

  9. The probabilities of solving a problem correctly by A and B are (1)/(8...

    Text Solution

    |

  10. The probability of event A is 3//4. The probability of event B, given ...

    Text Solution

    |

  11. An urn contains three white, six red and four black balls. Two balls a...

    Text Solution

    |

  12. Let A,B,C be 3 events such that P(A//B)=(1)/(5), P(B)=(1)/(2), P(A//C)...

    Text Solution

    |

  13. A coin is tossed. If head appears a fair die is thrown three times oth...

    Text Solution

    |

  14. For any events A and B. Given P(AuuB)=0.6, P(A)=P(B)=0.4, Then the val...

    Text Solution

    |

  15. Mohan post a letter to Sohan. It is known that one letter out of 10 le...

    Text Solution

    |

  16. If E(1) and E(2) are two events such that P(E(1))=1//4, P(E(2)//E(1))=...

    Text Solution

    |

  17. P(A)=3//8; P(B)=1//2; P(AuuB)=5//8 , which of the following do/does ho...

    Text Solution

    |

  18. Consider the word POSSIBILITY. In the arrangement of the letters of th...

    Text Solution

    |

  19. A slip of paper is given to a person A who marks it either with a plus...

    Text Solution

    |

  20. A slip of paper is given to a person A who marks it either with a plus...

    Text Solution

    |