Home
Class 12
MATHS
Three randomly chosen nonnegative intege...

Three randomly chosen nonnegative integers `x , ya n dz` are found to satisfy the equation `x+y+z=10.` Then the probability that `z` is even, is: `5/(12)` (b) `1/2` (c) `6/(11)` (d) `(36)/(55)`

A

`(1)/(2)`

B

`(36)/(55)`

C

`(6)/(11)`

D

`(5)/(11)`

Text Solution

Verified by Experts

The correct Answer is:
C
`x + y + z = 10`
Total number of non-negative solutions = `.^(10+3-1)C_(3-1) = .^(12)C_(2) = 66`
Now let z = 2n
`therefore x + y = 10 - 2n, n ge 0`
Number of non-negative solutions of above equation is
11 + 9 + 7 + 5 + 3 + 1 = 36.
`therefore` Required probability = `(36)/(66) = (6)/(11)`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY I

    CENGAGE ENGLISH|Exercise ARCHIVES|4 Videos

  • PROBABILITY

    CENGAGE ENGLISH|Exercise Comprehension|2 Videos

  • PROBABILITY II

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

Similar Questions

Explore conceptually related problems

The number of nonnegative integer solutions of the equation x+y+z+5t = 15 is

Find the number of triplets (x, y, z) of integers satisfying the equations x + y = 1 - z and x^(3) + y^(3) =1-z^(2) (where z ne 1 )

Solve the system of equations in x,y and z satisfying the following equations x+[y]+{z}=3.1, y+[z]+{x}=4.3 and z+[x]+{y}=5.4

If z_1a n dz_2 are the complex roots of the equation (x-3)^3+1=0,t h e nz_1+z_2 equal to 1 b. 3 c. 5 d. 7

x=36z y=36z^(2)+5 If z gt 0 in the equations above, what is y in terms of x?

If x , ya n dz are the distances of incenter from the vertices of the triangle A B C , respectively, then prove that (a b c)/(x y z)=cot(A/2)cot(B/2)cot(C/2)

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove that x ,a n d4,z are in H.P.

If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove that x ,a n d4,z are in H.P.

Consider the equation x^3-3x^2+2x=0, then (a)Number of even integers satisfying the equation is 2 (b)Number of odd integers satisfying the equation is 1 (c)Number of odd prime natural satisfying the equation is 1 (d)Number of composite natural numbers satisfying the equation is 1