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Let p be the probability of happeni...

Let p be the probability of happening of an event , and q of its non- happening then the total chance of r successes in n trials ` 0 le r le n , ` is

A

`""^(n )C_(r) .p^(r) . q^(n-r)`

B

`""^(n)C_(r).p^(r-1).q^(r+1)`

C

`""^(n)C_(r).P^(r+1).q^(r-1)`

D

`""^(n)C_(r).P^(r ).q^(r )`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • A positive integer 'n' not exceeding 100, is chosen in such a way that if n le 50 , then the probability of chossing n is 'p' , and if n gt 50 , then the probability of choising n is '3p'. The probability that a perfect square is chosen is

    A
    0.08
    B
    0.065
    C
    0.05
    D
    0.09

  • IF 0 lt r lt s le n and ""^n P_r = "^n P_s then the value of r+s is

    A
    1
    B
    2
    C
    `2n-1`
    D
    `2n-2`

  • In a series of n independent trials for an event of consist probability p, the most probable number r of successes is given by (n+1)p-1 lt r lt (n+1)p . Hence the most probable number of successes is the integral part of (n+1) p, But if (n+1) p is an integer the chance of r successes is equal to that of (r+1) successes and bot r,r+1 are most problem number of successes. A bag contains 2 white and 1 black balls. A ball is drawn at random and returned to bag. The experiment id done 5 times. The probability that a white ball is drawn most of the time is.

    A
    `(8)/(81)`
    B
    `9((2)/(3))^6`
    C
    `((2)/(3))^6`
    D
    `(8)/(27)`.

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    In a series of n independent trials for an event of consist probability p, the most probable number r of successes is given by (n+1)p-1 lt r lt (n+1)p . Hence the most probable number of successes is the integral part of (n+1) p, But if (n+1) p is an integer the chance of r successes is equal to that of (r+1) successes and bot r,r+1 are most problem number of successes. A bag contains 2 white and 1 black balls. A ball is drawn at random and returned to bag. The experiment is done 10 times. The probability that a white ball is drawn exactly 5 times is .

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