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Binomial Distribution Maths - Binomial Distribution

Maharashtra Board - STD 12 - Maths (MSBSHSE - Semi English Medium). 135 questions in this chapter.

Question types

Binomial Distribution question types

135 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

135
Questions
4
Question groups
5
Question types
Sample Questions

Binomial Distribution questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
If $X$ is a binomial variate with parameters $n$ and $p$, where $0 < p < 1$ such that $\frac{\text{P(X = r)}}{\text{P(X = n - r})}$ is independent of $n$ and $r,$ then $p$ equals:
  • ✓
    $\frac{1}{2}$
  • B
    $\frac{1}{3}$
  • C
    $\frac{1}{4}$
  • D
    $\text{None of these}$

Answer: A.

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Q 2MCQ1 Mark
In a box containing $100$ bulbs, $10$ are defective. What is the probability that out of a sample of $5$ bulbs, none is defective?
  • ✓
    $\big(\frac{9}{10}\big)^5$
  • B
    $\frac{9}{10}$
  • C
    $10^{-5}$
  • D
    $\big(\frac{1}{2}\big)^2$

Answer: A.

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Q 3MCQ1 Mark
A five$-$digit number is written down at raddom. The probability that the number is divisible by $5$, and no two consecutive digits are identical, is:
  • A
    $\frac{1}{5}$
  • ✓
    $\frac{1}{5}\big(\frac{9}{10}\big)^3$
  • C
    $\big(\frac{3}{5}\big)^4$
  • D
    $\text{None of these}$

Answer: B.

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Q 4MCQ1 Mark
If the mean and variance of a binomial distribution are $4$ and $3$, respectively, the probability of getting exactly six successes in this distribution is:
  • A
    $\text{ }^{16}\text{C}_6\big(\frac{1}{4}\big)^{10}\big(\frac{3}{4}\big)^6$
  • ✓
    $\text{ }^{16}\text{C}_6\big(\frac{1}{4}\big)^{6}\big(\frac{3}{4}\big)^{10}$
  • C
    $\text{ }^{12}\text{C}_6\big(\frac{1}{20}\big)\big(\frac{3}{4}\big)^6$
  • D
    $\text{ }^{12}\text{C}_6\big(\frac{1}{20}\big)^6\big(\frac{3}{4}\big)^6$

Answer: B.

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Q 5MCQ1 Mark
If the mean and variance of a binomial variate $X$ are $2$ and $1$ respectively, then the probability that $X$ takes a value greater than $1$ is:
  • A
    $\frac{2}{3}$
  • B
    $\frac{4}{5}$
  • C
    $\frac{7}{8}$
  • ✓
    $\frac{15}{16}$

Answer: D.

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Q 14Solve the Following Question.(3 Marks)3 Marks
A man wins a rupee for head and loses a rupee for tail when a coin is tossed. Suppose that he tosses once and quits if he wins but tries once more if he loses on the first toss. Find the probability distribution of the number of rupees the man wins.
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