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JEE Advanced 2017Paper 2
Exam
JEE Advanced
Year
2017
Paper
Paper 2
Subject
Mathematics
Chapter
Probability

JEE Advanced 2017 · Paper 2 · Mathematics · Probability

Three randomly chosen non negative integers x, y, z are found to...

Three randomly chosen non negative integers x,y,zx, y, z are found to satisfy the equation x+y+z=10x + y + z = 10 . Then the probability that zz is even, is

Options

  1. A3655\dfrac{36}{55}
  2. B611\dfrac{6}{11}
  3. C511\dfrac{5}{11}
  4. D12\dfrac{1}{2}

Correct answer

B. 611\dfrac{6}{11}

Step-by-step solution

Let z=2k,z = 2k, where k=0,1,2,3,4,5k = 0, 1, 2, 3, 4, 5

∴x+y=10−2k∴ x + y = 10 - 2k

Number of non negative integral solutions

∑k=0511−2kC1=∑11−2k=36\mathop{∑}_{k = 0}^{5}{}^{11 - 2k}{C}_{1} = ∑ 11 - 2k = 36

Total cases =10+3−1C3−1=66= {}^{10 + 3 - 1}{C}_{3 - 1} = 66

Required probability =3666=611= \dfrac{36}{66} = \dfrac{6}{11}

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