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Probability Applied Maths - Probability

CBSE - STD 12 Science - Applied Maths (CBSE - English Medium). 104 questions in this chapter.

Question types

Probability question types

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

104
Questions
5
Question groups
5
Question types
Sample Questions

Probability 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
The $pdf$ of Poisson Distribution is given by __________
  • ✓
    $\frac{e^{-m} m^x}{x!}$
  • B
    $\frac{e^{-m} x!}{m^x}$
  • C
    $\frac{x!}{m^x e^{-m}}$
  • D
    $\frac{e^m m^x}{x!}$

Answer: A.

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Q 2MCQ1 Mark
If '$m$' is the mean of Poisson Distribution, the standard. deviation is given by __________.
  • ✓
    $\sqrt{m}$
  • B
    $m^2$
  • C
    $m$
  • D
    $\frac{m}{2}$

Answer: A.

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Q 3MCQ1 Mark
If '$m$' is the mean of a Poisson Distribution, then variance is given by _________.
  • A
    $m^2$
  • B
    $m^{1 / 2}$
  • ✓
    $m$
  • D
    $\frac{m}{2}$

Answer: C.

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Q 4MCQ1 Mark
For larger values of '$n$', Binomial Distribution __________.
  • A
    loses its discreteness
  • ✓
    tends to Poisson's Distribution
  • C
    Stays as it is
  • D
    gives oscillatory values

Answer: B.

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Q 5MCQ1 Mark
Binomial distribution is a _________
  • A
    Continuous distribution
  • ✓
    Discrete distribution
  • C
    Irregular distribution
  • D
    Not a Probability distribution

Answer: B.

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Q 62 Marks Questions2 Marks
For some computers, the time period between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. Rohan has one of these computers and needs to know the probability that the time period will be between 50 and 70 hours.
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Q 72 Marks Questions2 Marks
The speeds of cars are measure using a radar unit, on a motorway. The speeds are normally distributed with a mean of $90$ km/hr and a standard deviation of $10$ km/hr. What is the probability that a car selected at chance is moving at more than $100$ km/hr?
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Q 82 Marks Questions2 Marks
Assume the mean height of children to be $69.25$ cm with a variance of $10.8$ cm. How many children in a school of $1,200$ would you expect to be over $74$ cm tall?
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Q 92 Marks Questions2 Marks
The average daily procurement of milk by village society in 800 litres with a standard deviation of 100 litres. Find out proportion of societies procuring milk between 800 litres to 1000 litres per day.
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Q 102 Marks Questions2 Marks
Weights of fish caught by a traveller are approximately normally distributed with a mean weight of $2.25$ kg and a standard deviation of $0.25$ kg. What percentage of fish weigh less than $2$ kg?
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Q 113 Marks Question3 Marks
A bank manager has observed that the length of time the customers have to wait for being attended by the teller is normally distribution with mean time of 5 minutes and standard deviation of 0.7 minutes. Find the probability that a customer has to wait
(i) for less than 6 minutes
(ii) between 3.5 and 6.5 minutes
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Q 123 Marks Question3 Marks
Assume that the mean height of soldiers is 69.25 inches with a variance of 9.8 inches. How many soldiers in a regiment of 6,000 would you expect to be over 6 feet tall?
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Q 133 Marks Question3 Marks
900 light bulbs with a mean life of 125 days are installed in a new factory. Their length of life is normally distributed with a standard deviation of 18 days. What is the expected number of bulbs expire in less than 95 days?
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Q 143 Marks Question3 Marks
The marks obtained in a certain exam follow normal distribution with mean 45 and SD 10. If 1,300 students appeared at the examination, calculate the number of students scoring (i) less than 35 marks and (ii) more than 65 marks.
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Q 153 Marks Question3 Marks
Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of diamond cards drawn. Also, find the mean and the variance of the distribution.
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Q 165 Marks Questions5 Marks
A sample of 125 dry battery cells tested to find the length of life produced the following results with mean 12 and SD 3 hours. Assuming that the data to be normal distributed, what percentage of battery cells are expected to have life
(i) more than 13 hours
(ii) less than 5 hours
(iii) between 9 and 14 hours
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Q 175 Marks Questions5 Marks
The average daily sale of 550 branch offices was ₹ 150 thousand and standard deviation is ₹ 15 thousand. Assuming the distribution to be normal, indicate how many branches have sales between
(i) ₹ 1,25,000 and ₹ 1,45,000
(ii) ₹ 1,40,000 and ₹ 1,60,000
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Q 205 Marks Questions5 Marks
In the proportion of defective in a bulk is 4%. Find the probability of not more than 2 defective in a sample of 10. It is known that $e^{-4}=0.6703.$
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Q 21Case study (4 Marks)4 Marks
Read the following text and answer the following questions on the basis of the same:
Today in mathematics class Mr. Lal teaches the topic of Binomial distribution. Four friends Rohan, Rohit, Roshan and Raman have few doubts in this topic, so they decided for group study at Rohan's place. They are trying to solve a question in which a pair of dice is thrown 7 times. If getting a total 7 is considered a success, then answer the following questions:
Image
Q.1. If X denote the number of success in 7 throws of a pair of dice, then X Binomial variate with parameters:
(A) $n=7, p=\frac{1}{6}\quad$ (B) $n=2, p=\frac{1}{6}\quad$ (C) $n=7, p=\frac{5}{6}\quad$ (D) $n=2, p=\frac{5}{6}$
Q.2. What is the probability of no success?
(A) $\left(\frac{6}{5}\right)^7\quad$ (B) $\left(\frac{5}{6}\right)^7\quad$ (C) $\left(\frac{1}{5}\right)^7\quad$ (D) $\left(\frac{5}{6}\right)\quad$
Q.3. What is the probability of 6 success?
(A) $\left(\frac{1}{6}\right)^7\quad$ (B) $35\left(\frac{1}{6}\right)\quad$ (C) $35\left(\frac{1}{6}\right)^7\quad$ (D) $35\left(\frac{5}{6}\right)^7\quad$
Q.4. What is the probability of at least 6 success?
(A) $\left(\frac{1}{6}\right)^5\quad$ (B) $\left(\frac{1}{6}\right)^7\quad$ (C) $\left(\frac{1}{6}\right)^6\quad$ (D) $\left(\frac{5}{6}\right)^5$
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Q 22Case study (4 Marks)4 Marks
Read the following text and answer the following questions on the basis of the same:
We take 8 identical slips of paper; write the number 0 on one of them, the number 1 on three of the slips, the number 2 on three of the slips and the number 3 on one of the slip. These slips are folded, put in a box and thoroughly mixed. One slip is drawn at random from the box. If X is the random variable denoting the number written on the drawn slip, answer the following questions:
Image
Q.1. How many total values X can take?
(A) 1 $\quad$ (B) 2 $\quad$ (C) 3 $\quad$ (D) 4
Q.2. Find the probability when X = 0.
(A) $\frac{1}{8}$ $\quad$ (B) $\frac{3}{8}$ $\quad$ (C) $\frac{1}{2}$ $\quad$ (D) $\frac{1}{4}$
Q.3. Find the probability when X = 1.
(A) $\frac{1}{8}$ $\quad$ (B) $\frac{3}{8}$ $\quad$ (C) $\frac{1}{2}$ $\quad$ (D) $\frac{1}{4}$
Q.4. The probability distribution is given as:
Image
Image
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Q 23Case study (4 Marks)4 Marks
Read the following text and answer the following questions on the basis of the same:
Mr. Rama Roy a owner of a factory lives in Karnataka. In his factory, he manufactures razor blades. There is a small chance that $\frac{1}{500}$ for any blade to be defective. The blades are in the packets of 10.
Image
Q.1. The probability that packet contain no defective blade is:
(A) $e^{-0.02}$
(B) $0.02$
(C) $0.02~ e^{-0.02}$
(D) $0.002 ~e^{-0.02}$
Q.2. The probability that packet contain one defective blade is:
(A) $e^{-0.02}$
(B) $0.02 e^{-0.02}$
(C) $0.02 e^{-0.002}$
(D) $0.002 e^{-0.02}$
Q.3. Find the probability that packet contain two detective blade, when it is given that $e^{-0.02}=0.9802$
(A) 0.0002 $\quad$ (B) 0.002 $\quad$ (C) 0.2 $\quad$ (D) None of these
Q.4. Find the approximate number of packets containing no defective blade, when there are 10000 packets in a consignment. $\quad\quad (\text{Use }e^{-0.02}=0.9802)$
(A) 9802 $\quad$ (B) 9800 $\quad$ (C) 2 $\quad$ (D) 196
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