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Probability Maths - Probability

Jharkhand Board (JAC) - STD 9 - Maths (Jharkhand - English Medium). 33 questions in this chapter.

Question types

Probability question types

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

33
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 1M.C.Q1 Mark
$80$ bulbs are selected at random from a lot and their lifetime in hours is recorded as under.
Lifetime (in hours)
$300$
$500$
$700$
$900$
$1100$
Frequency
$10$
$12$
$23$
$25$
$10$
One bulb is selected at random from the lot. What is the probability that the selected bulb has a life more than $500$ hours$?$
  • A
    $\frac{27}{40}$
  • ✓
    $\frac{29}{40}$
  • C
    $\frac{5}{16}$
  • D
    $\frac{11}{40}$

Answer: B.

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Q 2M.C.Q1 Mark
Two coins are tossed simultaneously $600$ times to get: $2$ heads : $234$ times, $1$ head : $206$ times, $0$ head : $160$ times. If two coins are tossed at random, what is the probability of getting at least one head$?$
  • A
    $\frac{103}{300}$
  • B
    $\frac{39}{100}$
  • ✓
    $\frac{11}{15}$
  • D
    $\frac{4}{15}$

Answer: C.

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Q 3M.C.Q1 Mark
In a survey of $364$ children aged $19 - 36$ months, it was found that $91$ liked to eat potato chips. If a child is selected at random, the probability that he / she does not like to eat potato chips is:
  • A
    $\frac{1}{4}$
  • B
    $\frac{1}{2}$
  • ✓
    $\frac{3}{4}$
  • D
    $\frac{4}{5}$

Answer: C.

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Q 4M.C.Q1 Mark
In a medical examination of students of a class, the following blood groups are recorded:
Blood group
$A$
$B$
$AB$
$O$
Number of students
$11$
$15$
$8$
$6$
From this class, a student is chosen at random. What is the probability that the chosen student has blood group $AB?$
  • A
    $\frac{13}{20}$
  • B
    $\frac{3}{8}$
  • ✓
    $\frac{1}{5}$
  • D
    $\frac{11}{40}$

Answer: C.

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Q 5M.C.Q1 Mark
It is given that the probability of winning a game is $0.7.$ What is the probability of losing the game$?$
  • A
    $0.8$
  • ✓
    $0.3$
  • C
    $0.35$
  • D
    $0.15$

Answer: B.

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Q 62 Marks Questions2 Marks
The percentages of marks obtained by a student in six unit tests are given below:
Unit test
$I$
$II$
$III$
$IV$
$V$
$VI$
Percentage of marks obtained
$53$
$72$
$28$
$46$
$67$
$59$
A unit test is selected at random. What is the probability that the student gets more than 60% marks in the test?
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Q 72 Marks Questions2 Marks
The marks obtained by $90$ students of a school in mathematics out of $100$ are given as under:
Marks
$0 - 20$
$20 - 30$
$30 - 40$
$40 - 50$
$50 - 60$
$60 - 70$
$70$ and above
Number of students
$7$
$8$
$12$
$25$
$19$
$10$
$9$
From these students, a student is chosen at random. What is the probability that the chosen student:
$i. $Gets $20\%$ or less marks?
$ii$. Gets $60\%$ or more marks?
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Q 82 Marks Questions2 Marks
On a particular day, at a crossing in a city, the various types of $240$ vehicles going past during a time interval were observed, as under:
Types of vehicle
Two-wheelers
Three-wheelers
Four-wheelers
Frequency
$84$
$68$
$88$
Out of these vehicles, one is chosen at random. What is the probability that the chosen vehicle is a two-wheeler?
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Q 92 Marks Questions2 Marks
$12$ Packets of salt, each marked 2kg, actually contained the following weights (in kg) of salt:
$1.950, 2.020, 2.060, 1.980, 2.030, 1.970, 2.040, 1.990, 1.985, 2.025, 2.000, 1.980.$
Out of these packets, one packet is chosen at random.
What is the probability that the chosen packet contains more than $2\ kg$ of salt?
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Q 113 Marks Question3 Marks
On one page of a telephone directory, there are $200$ phone numbers. The frequency distribution of their unit's digits is given below:
Unit's digit $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$
Frequency $19$ $22$ $23$ $19$ $21$ $24$ $23$ $18$ $16$ $15$
One of the numbers is chosen at random from the page. What is the probability that the unit's digit of the chosen number is:
$i. 5?$
$ii. 8?$
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Q 123 Marks Question3 Marks
The following table shows the blood groups of $40$ students of a class.
Blood group $A$ $B$ $O$ $AB$
Number of students $11$ $9$ $14$ $6$
One student of the class is chosen at random. What is the probability that the chosen students blood group is:
$i. O?$
$ii. AB?$
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Q 133 Marks Question3 Marks
The table given below shows the marks obtained by $30$ students in a test.
Marks
$($Class interval$)$		 $1 - 10$ $11 - 20$ $21 - 30$ $31 - 40$ $41 - 50$
Number of students
$($Frequency$)$		 $7$ $10$ $6$ $4$ $3$
Out of these students, one is chosen at random. What is the probability that the marks of the chosen student:
$i.$ Are $30$ or less?
$ii.$ Are $31$ or more?
$iii.$ Lie in the interval $21 - 30$?
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Q 143 Marks Question3 Marks
It is known that a box of $800$ electric bulbs contains $36$ defective bulbs.One bulb is taken at random out of the box. What is the probability that the bulb chosen is non-defective?
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Q 155 Marks Questions5 Marks
The table given below shows the ages of $75$ teachers in a school.
Age $($in years$)$
$18 - 29$
$30 - 39$
$40 - 49$
$50 - 59$
Number of teachers
$3$
$27$
$37$
$8$
A teacher from this school is chosen at random. What is the probability that the selected teacher is:
$i. 40$ or more than $40$ years old$?$
$ii.$ Of an age lying between $30 - 39$ years $($including both$)?$
$iii. 18$ years or more and $49$ years or less$?$
$iv. 18$ years or more old$?$
$v.$  Above $60$ years of age$?$
Note: Here $18 - 29$ means $18$ or more but less than or equal to $29.$
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Q 165 Marks Questions5 Marks
An organisation selected $2400$ families at random and surveyed them to determine a relationship between the income level and the number of vehicles in a family. The information gathered is listed in the table below:
Monthly income$($in $₹)$
Number of vehicles per family
$0$
$1$
$2$
$3$ or more
Less than $₹ 25000$
$10$
$160$
$25$
$0$
$₹ 25000 - ₹ 30000$
$0$
$305$
$27$
$2$
$₹ 30000 - ₹ 35000$
$1$
$535$
$29$
$1$
$₹ 35000 - ₹ 40000$
$2$
$469$
$59$
$25$
$₹ 40000$ or more
$1$
$579$
$82$
$88$
Suppose a family is chosen at random. Find the probability that the family chosen is:
$i.$ Earning $₹ 25000 - ₹ 30000$ per month and owning exactly $2$ vehicles.
$ii.$ Earning $₹ 40000$ or more per month and owning exactly $1$ vehicle.
$iii.$ Earning less than $₹ 25000$ per month and not owning any vehicle.
$iv.$ Earning $₹ 35000 - ₹ 40000$ per month and owning $ 2$ or more vehicles.
$v.$ Owning not more than $1$ vehicle.
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Q 175 Marks Questions5 Marks
Following are the ages $($in years$)$ of $360$ patients, getting medical treatment in a hospital:
Age $($in years$)$
$10 - 20$
$20 - 30$
$30 - 40$
$40 - 50$
$50 - 60$
$60 - 70$
Number of patients
$90$
$50$
$60$
$80$
$50$
$30$
One of the patients is selected at random. What is the probability that his age is:
$i. 30$ years or more but less than $40$ years$?$
$ii. 50$ years or more but less than $70$ years$?$
$iii.10$ years or more but less than $40$ years$?$
$iv. 10$ years or more$?$
$v.$ Less than $10$ years$?$
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Q 184 Marks Questions4 Marks
Two coins are tossed $400$ times and we get: Two heads: $112$ times; one head: $160$ times; $0$ head: $128$ times. When two coins are tossed at random, what is the probability of getting
$i. 2$ heads?
$ii. 1$ heads?
$iii. 0$ heads?
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Q 194 Marks Questions4 Marks
A die is thrown $300$ times and the outcomes are noted as given below:
Outcome
$1$
$2$
$3$
$4$
$5$
$6$
Frequency
$60$
$72$
$54$
$42$
$39$
$33$
When a dice is thrown at random, what is the probability of getting a
  • A
    $3?$
  • B
    $6?$
  • C
    $5?$
  • D
    $1?$
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Q 204 Marks Questions4 Marks
Three coins are tossed $200$ times and we get: Three heads: $39$ times; two heads: $58$ times; One head: $67$ times; $0$ head: $36$ times. When three coins are tossed at random, what is the probability of getting
  • A
    $3$ heads?
  • B
    $1$ heads?
  • C
    $0$ heads?
  • D
    $2$ heads?
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