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Binomial Distribution MATHS - Binomial Distribution

Rajasthan Board (RBSE) - STD 12 Science - MATHS (Rajasthan - 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:
  1. $\frac{1}{2}$
  2. $\frac{1}{3}$
  3. $\frac{1}{4}$
  4. $\text{None of these}$
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Q 2M.C.Q (1 Marks)1 Mark
Mark the correct alternative in the following question:The probability of guessing correctly at least 8 out of 10 answers of a true false type examination is:
  1. $\frac{7}{64}$
  2. $\frac{7}{128}$
  3. $\frac{45}{1024}$
  4. $\frac{7}{41}$
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Q 3M.C.Q (1 Marks)1 Mark
Mark the correct alternative in the following question:Which one is not a requirement of a binomial dstribution?
  1. There are 2 outcomes for each trial.
  2. There is a fixed number of trials.
  3. The outcomes must be dependent on each other.
  4. The probability of success must be the same for all the trials.
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Q 4M.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?
  1. $\big(\frac{9}{10}\big)^5$
  2. $\frac{9}{10}$
  3. $10^{-5}$
  4. $\big(\frac{1}{2}\big)^2$
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Q 5M.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:
  1. $\text{ }^{16}\text{C}_6\big(\frac{1}{4}\big)^{10}\big(\frac{3}{4}\big)^6$
  2. $\text{ }^{16}\text{C}_6\big(\frac{1}{4}\big)^{6}\big(\frac{3}{4}\big)^{10}$
  3. $\text{ }^{12}\text{C}_6\big(\frac{1}{20}\big)\big(\frac{3}{4}\big)^6$
  4. $\text{ }^{12}\text{C}_6\big(\frac{1}{20}\big)^6\big(\frac{3}{4}\big)^6$
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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 133 Marks Question3 Marks
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes and, hence, find its mean.
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Q 143 Marks Question3 Marks
Five dice are thrown simultaneously. If the occurrence of 3, 4 or 5 in a single die is considered a success, find the probability of at least 3 successes.
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Q 153 Marks Question3 Marks
The probability is 0.02 that an item produced by a factory is defective. A shipment of 10,000 items is sent to its warehouse. Find the expected number of defective items and the standard deviation.
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Q 163 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 195 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 205 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 215 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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