Home
Class 12
MATHS
The sum of two positive quantities is eq...

The sum of two positive quantities is equal to `2ndot` the probability that their product is not less than 3/4 times their greatest product is `3//4` b. `1//4` c. `1//2` d. none of these

Text Solution

Verified by Experts

Let one of the quantities be x.
Then the other quantity will be 2n - x.
Their product will be greatest when they are equal, i.e., each is n. In this case, the product is `n^(2)`.
According to the proposition.
`x(2n - x) ge (3)/(4) n^(2)`
`implies 4x^(2) - 8nx + 3n^(2) le 0`
`implies (2x - 3n) (2x-n) le0`
`implies (n)/(2) le x le (3)/(2)n`
So, number of favourable cases is equivalents to the length of the interval `[n//2, 3n//2]`, which is n.
Also, `x in (0, 2n)`.
So, total number of cases is equivalent to length of the interval (0, 2n).
`therefore` Required probability = `(n)/(2n) = (1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY I

    CENGAGE PUBLICATION|Exercise Exercise 9.1|6 Videos

  • PROBABILITY I

    CENGAGE PUBLICATION|Exercise Exercise 9.2|19 Videos

  • PROBABILITY I

    CENGAGE PUBLICATION|Exercise JEE Advanced|7 Videos

  • PROBABILITY

    CENGAGE PUBLICATION|Exercise All Questions|470 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

Similar Questions

Explore conceptually related problems

The sum of two positive quantities is equal to 2ndot the probability that their product is not less than 3/4 times their greatest product is a. 3//4 b. 1//4 c. 1//2 d. none of these

if the product of two positive quantities be given, their sum is least , when they are equal.

Using calculus prove that , if the sum of two positive quantities be given , their product is maximum , when they are equal ,

If the sum to infinity of the series 1+2r+3r^2+4r^3+ is 9/4, then value of r is (a) 1//2 b. 1//3 c. 1//4 d. none of these

A four figure number is formed of the figures 1, 2, 3, 4, 5 with no repetitions. The probability that the number is divisible by 5 is 3//4 b. 1//4 c. 1//8 d. none of these

A father has 3 children with at least one boy. The probability that he has 2 boys and 1 girl is a. 1//4 b. 1//3 c. 2//3 d. none of these

If n integers taken at random are multiplied together , then the probability that the last digit of the product is 1, 3, 7, or 9 is a. 2^n//5^n b. 4^n-2^n//5^n c. 4^n//5^n d. none of these

A 2n digit number starts with 2 and all its digits are prime, then the probability that the sum of all 2 consecutive digits of the number is prime is a. 4xx2^(3n) b. 4xx2^(-3n) c. 2^(3n) d. none of these

A draws a card from a pack of n cards marked 1,2,ddot,ndot The card is replaced in the pack and B draws a card. Then the probability that A draws a higher card than B is (n+1)//2n b. 1//2 c. (n-1)//2n d. none of these

Four die are thrown simultaneously. The probability that 4 and 3 appear on two of the die given that 5 and 6 have appeared on other two die is a) 1/6 b) 1/36 c) 12/151 d) none of these