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:

A

`(1)/(2)`

B

`(36)/(55)`

C

`(6)/(11)`

D

`(5)/(11)`

Text Solution

Verified by Experts

The correct Answer is:
C
Sample space `rarr ^(12)C_2`
Number of possible for Z is even `z=0 rArr^(11)C_1`
`z=2 rArr^(9)C_1`
`z=4 rArr^(7)C_1`
`z=6 rArr^(5)C_1`
`z=8 rArr^(3)C_1`
`z=0 rArr^(1)C_1`
Total =36
`therefore " Probility " =(36)/(66)=6/(11)`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 1 CLASSICAL PROBABLITY OBJECTIVE QUESTIONS I (ASSERTION AND REASON)|2 Videos

  • PROBABILITY

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 1 CLASSICAL PROBABLITY OBJECTIVE QUESTIONS I (PASSAGE BASED PROBLEMS )|1 Videos

  • PERMUTATIONS AND COMBINATIONS

    IIT JEE PREVIOUS YEAR|Exercise Dearrangement and Number of Divisors (Fill in the Blank )|1 Videos

  • RELATIONS AND FUNCTIONS

    IIT JEE PREVIOUS YEAR|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

Three randomly chosen nonnegative integers x,y and z 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)

Two non-negative integers x and y are chosen at random with replacement. The probability that x^(2)+y^(2) is divisible by 10, is

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

The number of non-negative integer solutions of the equations 6x+4y+z=200 and x+y+z=100 is

Three integers are chosen at random from the first 20 integers. The probability that their product is even, is

Three integers are chosen at random from the first 20 integers.The probability that their product is even is:

If x,y,z in N. Then the probability that x^(2)+y^(2)+z^(z) is divisible by 7 is

The number of solutions of the equation x+y+z =10 in positive integers x,y,z is equal to

If n is a positive integer greater than unity z is a complex number satisfying the equation z^(n)=(z+1)^(n), then

IIT JEE PREVIOUS YEAR-PROBABILITY-TOPIC 5 PROBABILITY DISTRIBUTION AND BINOMIAL DISTRIBUTTION OBJECTIVE QUESTIONS ONLY ONE CORRECT OPTION (INTEGER )
  1. Three randomly chosen nonnegative integers x , ya n dz are found to sa...

    Text Solution

    |

  2. The minimum number of times a fair coin needs to be tossed, so that th...

    Text Solution

    |