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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Probability

NDA 2019 · Mathematics · Probability

If a fair die is rolled 4 times, then what is the probability that...

If a fair die is rolled 4 times, then what is the probability that there are exactly 2 sixes?

Options

  1. A5216\frac{5}{216}
  2. B25216\frac{25}{216}
  3. C125216\frac{125}{216}
  4. D175216\frac{175}{216}

Correct answer

B. 25216\frac{25}{216}

Step-by-step solution

Given, n=4,p=16,q=56P(x=2)=4C2⋅p2⋅q2=6⋅(16)2(56)2=25216\begin{aligned} & n=4, p=\frac{1}{6}, q=\frac{5}{6} \\ & P(x=2)={ }^4 C_2 \cdot p^2 \cdot q^2 \\ & =6 \cdot\left(\frac{1}{6}\right)^2\left(\frac{5}{6}\right)^2 \\ & =\frac{25}{216} \end{aligned}
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