Home
Class 12
MATHS
If each element of a second order determ...

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive?
(Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability `1/2`)

Text Solution

AI Generated Solution

To solve the problem, we need to find the probability that the determinant of a second-order matrix (2x2 matrix) with entries either 0 or 1 is positive. ### Step-by-Step Solution: 1. **Define the Determinant**: For a 2x2 matrix with elements \( a, b, c, d \), the determinant is given by: \[ \text{Determinant} = ad - bc ...
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If each element of a second order determinant is either zero or one,what is the probability that the value the determinant is non- negative?

A determinant of second order of is made with the elements 0,1 . What is the probability that the determinant is positive?

A determinant of the second order is made with the elements 0 and 1. What is the probability that the determinant made is non-negative?

Minimum value of a second order determinant whose each is either 1 or 2 is equal to

If the entries in a 3xx3 determinant are either 0 or 1, then the greatest value of their determinants is

Find the value of the determinant: |(4,-2),(3,1)|

Minimum value of a second order determinant whose each entry is either 1or 2is equal to

If every element of a third order determinant of value Detlta is multiplied by 5, then the value of new determinant, is

NCERT-PROBABILITY-MISCELLANEOUS EXERCISE
  1. If A and B are any two events such that P(A) + P(B) - P(A a n d B) = P...

    Text Solution

    |

  2. If P(A|B) gt P(A), then which of the following is correct: (A) P(B |...

    Text Solution

    |

  3. A couple has two children,(i)    Find the probability that both childr...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. An urn contains 25 balls of which 10 balls bear a mark X and the rema...

    Text Solution

    |

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

    Text Solution

    |

  8. A die is thrown again and again until three sixes are obtained. Find ...

    Text Solution

    |

  9. An experiment succeeds twice as often as it fails. Find the probabili...

    Text Solution

    |

  10. If a leap year is selected at random, what is the chance that it will...

    Text Solution

    |

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

    Text Solution

    |

  12. A and B are two events such that P(A)!=0.Find P(B|A), if (i) A is a s...

    Text Solution

    |

  13. How many times must a man toss a fair com so that the probability of ...

    Text Solution

    |

  14. If A and B are two events such that P(A)!=0and P(B | A) = 1; then(A) A...

    Text Solution

    |

  15. Bag I contains 3 red and 4 black balls and Bag II contains 4 red and ...

    Text Solution

    |

  16. An electronic assembly consists of two subsystems, say, A and B. From...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |