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JKCET Binomial Distribution — practice questions

Explore 22 free Binomial Distribution questions in JKCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Binomial Distribution questions and exercises with answers

Showing questions 1–22 of 22.

If $X \sim B(n, p)$, the probability of exactly $x$ successes is:Read the answer and worked solution →For a Binomial distribution $X \sim B(n, p)$, the **mean** (expected value) is:Read the answer and worked solution →For a Binomial distribution $X \sim B(n, p)$, the **variance** is:Read the answer and worked solution →The **standard deviation** of $X \sim B(n, p)$ is:Read the answer and worked solution →If a fair coin is tossed $n$ times, the probability of any exact pattern (like all heads) is:Read the answer and worked solution →$P(X \geq 1) = 1 - P(X = 0)$ is an example of the:Read the answer and worked solution →If a die is thrown and 'getting an odd number' is success, then $p$ and $q$ are:Read the answer and worked solution →A fair coin is tossed 10 times. The probability of getting **exactly 6 heads** is:Read the answer and worked solution →A pair of dice is thrown 4 times. 'Getting a doublet' is a success. The probability of **exactly 2 successes** is:Read the answer and worked solution →Ten eggs drawn with replacement from a lot of 10% defective. Probability that **at least one** is defective:Read the answer and worked solution →If $X \sim B(10, 0.4)$, then $E(X)$ and $\text{Var}(X)$ are respectively:Read the answer and worked solution →If $E(X) = 6$ and $\text{Var}(X) = 4.2$ for $X \sim B(n, p)$, then $n$ and $p$ are:Read the answer and worked solution →A bag has balls marked 0–9. Four balls drawn with replacement. Probability that **none** is marked '0' is:Read the answer and worked solution →If $X \sim B(5, p)$ and $P(X = 4) = P(X = 3)$, then $p$ equals:Read the answer and worked solution →If $X \sim B(4, p)$ and $2P(X = 3) = 3P(X = 2)$, then $p$ equals:Read the answer and worked solution →A die is thrown 100 times; 'even number' is success. The standard deviation of the number of successes is:Read the answer and worked solution →Mean and variance of a binomial distribution are 4 and 2 respectively. The probability of **exactly 2** successes is:Read the answer and worked solution →Mean and variance of a binomial distribution are 18 and 12 respectively. The value of $n$ is:Read the answer and worked solution →If $X \sim B(4, p)$ and $P(X = 0) = 16/81$, then $P(X = 4)$ equals:Read the answer and worked solution →Probability of bomb hitting target = 0.8. Out of 10 bombs dropped, probability that **exactly 2 miss** equals (with $p = 0.2$ miss):Read the answer and worked solution →In a 5-trial binomial distribution, $P(X = 1) = 0.4096$ and $P(X = 2) = 0.2048$. The probability of success $p$ is:Read the answer and worked solution →Test what makes a trial binomialRead the answer and worked solution →

Worked practice questions

If $X \sim B(n, p)$, the probability of exactly $x$ successes is:

  1. ${}^nC_x p^x q^{n-x}$ where $q = 1 - p$
  2. $n \cdot p^x \cdot q^{n-x}$
  3. ${}^nC_x p q$
  4. $(p + q)^n$
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Correct answer: A. ${}^nC_x p^x q^{n-x}$ where $q = 1 - p$

Binomial p.m.f.: $P(X = x) = {}^nC_x \cdot p^x \cdot q^{n-x}$, where $q = 1 - p$. This is the $(x+1)^{th}$ term in the binomial expansion of $(q + p)^n$.

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For a Binomial distribution $X \sim B(n, p)$, the **mean** (expected value) is:

  1. $np$
  2. $npq$
  3. $\sqrt{npq}$
  4. $p/n$
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Correct answer: A. $np$

Mean $E(X) = np$. For a single Bernoulli trial $E = p$ by linearity, $n$ independent trials give $E = np$.

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For a Binomial distribution $X \sim B(n, p)$, the **variance** is:

  1. $np$
  2. $npq$ where $q = 1 - p$
  3. $\sqrt{np}$
  4. $n^2 p^2$
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Correct answer: B. $npq$ where $q = 1 - p$

Var$(X) = npq$. *Note: variance ≤ mean for binomial (since $q \le 1$), with equality only when $p = 0$.*

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More Mathematics topics

SequencesProbability & StatisticsBinomial TheoremSequences and SeriesGeometryLinear ProgrammingLimits and ContinuityPermutations and Combinations