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Three randomly chosen non-negative integ...

Three randomly chosen non-negative integers x, y and z 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)`
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