Home
Class 12
MATHS
Thirty-two players ranked 1 to 32 are pl...

Thirty-two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players the better ranked player wins, the probability that ranked 1 and ranked 2 players are winner and runner up respectively is p, then the value of `[2//p]` is, where [.] represents the greatest integer function,_____.

Text Solution

Verified by Experts

The correct Answer is:
3
For ranked 1 and 2 players to be winners and runners up, respectively, they should not be paired with each other in any round.
`impliesp=30/31xx14/15xx6/7xx2/3=16/31`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY II

    CENGAGE|Exercise JEE Main Previous Year|22 Videos

  • PROBABILITY II

    CENGAGE|Exercise LINKED COMPREHENSION TYPE|11 Videos

  • PROBABILITY II

    CENGAGE|Exercise Exercise (Matrix)|8 Videos

  • PROBABILITY I

    CENGAGE|Exercise JEE Advanced Previous Year|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

Similar Questions

Explore conceptually related problems

Thirty two players ranked 1 to 32 are playing is a knockout tournament. Assume that in every match between any two players, the better ranked player wins the probability that ranked 1 and ranked 2 players are winner and runner up, respectively, is (A) 16/31 (B) 1/2 (C) 17/31 (D) none of these

If a_1, a_2, a_3,54,a_6,a_7, a_8, a_9 are in H.P., and D=|a_1a_2a_3 4 5a_6a_7a_8a_9| , then the value of [D]i sw h e r e[dot] represents the greatest integer function

If a_1, a_2, a_3,54,a_6,a_7, a_8, a_9 are in H.P., and D=|a_1a_2a_3 5 4a_6a_7a_8a_9| , then the value of [D]i sw h e r e[dot] represents the greatest integer function

Consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1, and ("lim")_(xvec0)((p(x))/(x^3)-2)=4 . Then the value of [P(1)] is (where [.] represents greatest integer function)___

2^n players of equal strength are playing a knock out tournament. If they are paired at randomly in all rounds, find out the probability that out of two particular players S_1a n dS_2, exactly one will reach in semi-final (n in N ,ngeq2)dot

A dice is weighted such that the probability of rolling the face numbered n is proportional to n^(2) (n = 1, 2, 3, 4, 5, 6). The dice is rolled twice, yielding the number a and b. The probability that a gt b is p then the value of [2//p] (where [ . ] represents greatest integer function) is _______.

If two loaded dice each have the property that 2 or 4 is three times as likely to appear as 1, 3, 5, or 6 on each roll. When two such dice are rolled, the probability of obtaining a total of 7 is p , then the value of [1//p] is, where [x] represents the greatest integer less than or equal to xdot

Eight players P_1, P_2, P_3, ...........P_8 , play a knock out tournament. It is known that whenever the players P_i and P_j , play, the player P_i will win if i lt j . Assuming that the players are paired at random in each round, what is the probability that the players P_4 , reaches the final ?

8n players P_1, P_2, P_3, ,P_(8n) play a knock out tournament. It is known that all the players are of equal strength. The tournament is held in three rounds where the players are paired at random in each round. If it is given that P_1 Wins in the third round .Find the probability of P_2 loses in the second round.

The plane denoted by P_(1) : 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane P_(2) : 5x+3y+ 10 z = 25 . If the plane in its new position is denoted by P , and the distance of this plane from the origin is d, then find the value of [k//2] (where [*] represents greatest integer less than or equal to k).

CENGAGE-PROBABILITY II-Exercise (Numerical)
  1. If tow loaded dice each have the property that 2 or 4 is three times a...

    Text Solution

    |

  2. An urn contains three red balls and n white balls. Mr. A draws two bal...

    Text Solution

    |

  3. Suppose A and B are two events with P(A) = 0.5 and P(AuuB)=0.8LetP(B)=...

    Text Solution

    |

  4. Thirty-two players ranked 1 to 32 are playing in a knockout tournament...

    Text Solution

    |

  5. If Aa n dB are two events such that P(A)=0. 6 and P(B)=0. 8 , if the g...

    Text Solution

    |

  6. A die is thrown three times. The chance that the highest number shown ...

    Text Solution

    |

  7. Two cards are drawn from a well shuffled pack of 52 cards. The probabi...

    Text Solution

    |

  8. Find the derivative of y = 2 sin^3 (x^4).

    Text Solution

    |

  9. An unbiased normal coin is tossed n times. Let E(1): event that both...

    Text Solution

    |

  10. In a knockout tournament 2^n equally skilled players, S1,S2, S(2n) ar...

    Text Solution

    |

  11. If tow loaded dice each have the property that 2 or 4 is three times a...

    Text Solution

    |

  12. An urn contains three red balls and n white balls. Mr. A draws two bal...

    Text Solution

    |

  13. Suppose Aa n dB are two events with P(A)=0. 5a n dP(AuuB)=0. 8. Let P(...

    Text Solution

    |

  14. Thirty-two players ranked 1 to 32 are playing in a knockout tournament...

    Text Solution

    |

  15. If Aa n dB are two events such that P(A)=0. 6 and P(B)=0. 8 , if the g...

    Text Solution

    |

  16. A die is thrown three times. The chance that the highest number shown ...

    Text Solution

    |

  17. Two cards are drawn from a well shuffled pack of 52 cards. The probabi...

    Text Solution

    |

  18. A fair coin is flipped n times. Let E be the event "a head is obtained...

    Text Solution

    |

  19. An unbiased normal coin is tossed n times. Let E(1): event that both...

    Text Solution

    |

  20. In a knockout tournament 2^(n) equally skilled players, S(1),S(2),….S(...

    Text Solution

    |