Home
Class 11
MATHS
Prove that, if A1 and A2 are two events,...

Prove that, if `A_1` and `A_2` are two events, which are not necessarily mutually exclusive then `P(A_1 uu A_2) = P(A_1) + P(A_1 nn A_2)`

Promotional Banner

Topper's Solved these Questions

  • Model Test Set - 7

    UNITED BOOK HOUSE|Exercise Exercise |43 Videos

  • Model Test Set - 9

    UNITED BOOK HOUSE|Exercise Exercise |45 Videos

Similar Questions

Explore conceptually related problems

If A_1,A_2, A_3 , are equally likely, exhaustive and mutually exclusive then P(A_1) equals

If A_1 , A_2 , A_3 are mutually exclusive and exhaustive, then P(A_1) + P(A_2) + P(A_3) equal______

Show that P(B)>0 , then P(A_1 cup A_2|B) = P(A_1|B) + P(A_2|B)-P(A_1 cap A_2|B) .

Statement 1: if A={2,4,6,},B{1,5,3}w h e r eAa n dB are the events of numbers occurring on a dice, then P(A)+P(B)=1. Statement 2: A_1, A_2, A_3,...... , A_n are all mutually exclusive events, then P(A_1)+P(A_2)+.......+P(A_n)=1.

If P(A_1) = 0.2 , P(A_2) = 0.1 and P(A_3) = 0.3 and these events are mutually independent, then what is the value of P(A_1 nn A_2 nn A_3) ?

If P(A_1) = 0.3 , then P(A_1^C) = ?

For any two events A_1 and A_2 , prove that P(A_1 nn A_2) le min{PA_1),P(A_2)} where min {PA_1),P(A_2)} is the minimum of P(A_1) and P(A_2) .

For any two events A_1 and A_2 , show that P(A_1 cap A_2)lemin{P(A_1),P(A_2)} where min {P(A_1), P(A_2)} is the minimum of P(A_1) and P(A_2) .

A mixture consists of two radioactive materials A_1 and A_2 with half-lives of 20 s and 10 s respectively. Initially the mixture has 40 g of A_1 of 160 g of A_2 . After what time of amount of the two in the mixture will become equal ?

If a_1 and a_2 are two non-collinear unit vectors and if |a_1+a_2|=sqrt(3) , then the value of (a_1-a_2)*(2a_1+a_2) is

UNITED BOOK HOUSE-Model Test Set - 8-Exercise
  1. If P(A) = 1/2, P(B) = 2/3, then prove that 1/6 le P(A nn B) le 1/2.

    Text Solution

    |

  2. The probability of occurance of at least one of two events A and B is ...

    Text Solution

    |

  3. What are skewness and kurtosis?

    Text Solution

    |

  4. What is coefficient of variation? State its uses.

    Text Solution

    |

  5. Discuss about different sources of data on vital events.

    Text Solution

    |

  6. If x, y, z are positive quantities, prove that frac(x^3 + y^3)(x + y) ...

    Text Solution

    |

  7. Prove that there are no integers x, y such that x + y = 200 and greate...

    Text Solution

    |

  8. What do you mean by smog?

    Text Solution

    |

  9. If n is an odd integer, Prove that 16 is a divisor of n^4 + 4n^2 + 11.

    Text Solution

    |

  10. Write the classical definition of probability and state its limitation...

    Text Solution

    |

  11. Prove that, if A1 and A2 are two events, which are not necessarily mut...

    Text Solution

    |

  12. Find the probability that a leap year selected at random will contain ...

    Text Solution

    |

  13. Show that criide death rate can be expressed as weighted arithmetic me...

    Text Solution

    |

  14. Explain how would construct a cost of living index number (C.L.I)?

    Text Solution

    |

  15. In a frequency table, the upper boundary of each class-interval has a ...

    Text Solution

    |

  16. Write short note on FAO

    Text Solution

    |

  17. A letter is taken at random from the letters of the word STATISTICS an...

    Text Solution

    |

  18. If the letters of the word PROBABILITY are arranged at random, what is...

    Text Solution

    |

  19. Give a comparative study of the structures of diamond and graphite. Ex...

    Text Solution

    |

  20. Which colligative property is most suitable for the determination of m...

    Text Solution

    |