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Binomial Distribution Maths - Binomial Distribution

Uttarakhand Board (UBSE) - STD 12 Science - Maths (Uttarakhand - English Medium). 137 questions in this chapter.

Question types

Binomial Distribution question types

137 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

137
Questions
5
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 1M.C.Q (1 Marks)1 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 2M.C.Q (1 Marks)1 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 3M.C.Q (1 Marks)1 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 4M.C.Q (1 Marks)1 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:
  • ✓
    $\text{ }^{16}\text{C}_6\big(\frac{1}{4}\big)^{10}\big(\frac{3}{4}\big)^6$
  • B
    $\text{ }^{16}\text{C}_6\big(\frac{1}{4}\big)^{6}\big(\frac{3}{4}\big)^{10}$
  • 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: A.

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Q 5M.C.Q (1 Marks)1 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 72 Marks Questions2 Marks
A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that
any two are white?
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Q 92 Marks Questions2 Marks
A factory produces bulbs. The probability that one bulb is defective is $\frac{1}{50}$ and they are packed in boxes of 10. From a single box, find the probability that.
none of the bulbs is defective.
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Q 123 Marks Question3 Marks
There are 6% defective items in a large bulk of items. Find the probability that a sample of 8 items will include not more than one defective item.
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Q 153 Marks Question3 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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Q 163 Marks Question3 Marks
If the probability of a defective bolt is 0.1, find the (1) mean and (2) standard deviation for the distribution of bolts in a total of 400 bolts.
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Q 175 Marks Questions5 Marks
The probability that a certain kind of component will survive a given shock test is $\frac{3}{4}.$ Find the probability that among 5 components tested.
  1. exactly 2 will survive.
  2. at most 3 will survive.
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Q 185 Marks Questions5 Marks
A card is drawn and replaced in an ordinary pack of 52 cards. How many times must a card be drawn so that.
  1. there is at least an even chance of drawing a heart.
  2. the probability of drawing a heart is greater than $\frac{3}{4}$?
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Q 195 Marks Questions5 Marks
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $\frac{1}{100}.$ What is the probability that he will win a prize.
  1. at least once.
  2. exactly once.
  3. at least twice.
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