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JEE Main 202124 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
24 February
Shift
Morning Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2021 · 24 February · Morning Shift · Mathematics · Probability

An ordinary dice is rolled for a certain number of times. If the...

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 22 times is equal to the probability of getting an even number 33 times, then the probability of getting an odd number for odd number of times is:

Options

  1. A132\dfrac{1}{32}
  2. B516\dfrac{5}{16}
  3. C316\dfrac{3}{16}
  4. D12\dfrac{1}{2}

Correct answer

D. 12\dfrac{1}{2}

Step-by-step solution

C2n(12)n=C3n(12)n⇒C2n=C3nC2 n {\left(\dfrac{1}{2}\right)}^{n} = C3 n {\left(\dfrac{1}{2}\right)}^{n} ⇒ C2 n = C3 n

⇒n=5⇒ n = 5

Probability of getting an odd number for odd number of times is

C15(12)5+C35(12)5+C55(12)5=125(5+10+1)C1 5 {\left(\dfrac{1}{2}\right)}^{5} + C3 5 {\left(\dfrac{1}{2}\right)}^{5} + C5 5 {\left(\dfrac{1}{2}\right)}^{5} = \dfrac{1}{{2}^{5}}\left(5 + 10 + 1\right)

=12= \dfrac{1}{2}

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