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MATHS M.C.Q

Probability · MP Board (MPBSE) STD 9 (Madhya Pradesh - English Medium). 10 questions.

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M.C.Q

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10 questions · timed · auto-graded

MCQ 11 Mark
A dice is rolled $600$ times and the occurence of the outcomes $1, 2, 3, 4, 5$ and $6$ are given below:
Outcome
$1$
$2$
$3$
$4$
$5$
$6$
Frequency
$200$
$30$
$120$
$100$
$50$
$100$
The probability of geeting a prime number is:
  • ✓
    $\frac{1}{3}$
  • B
    $\frac{2}{3}$
  • C
    $\frac{49}{60}$
  • D
    $\frac{39}{125}$
Answer
Correct option: A.
$\frac{1}{3}$
Prime numbers in $1, 2, 3, 4, 5, 6$ are: $2, 3, 5.$
Number of times $2, 3, 5$ occur $= 30 + 120 + 50 = 200$
Total number of cases $= 200 + 30 + 120 + 100 + 50 + 100 = 600$
Required probability $=\frac{\text{Cases when we obtained (2, 3, 5)}}{\text{Total no. of cases}}$
$=\frac{200}{600}=\frac{1}{3}$
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MCQ 21 Mark
The probability of an event of a trial is:
  • A
    $1$
  • B
    $0$
  • ✓
    Less than $1$
  • D
    More than 0
Answer
Correct option: C.
Less than $1$
Probability of an event $=\frac{\text{No. of favorable cases}}{\text{Total no. of cases}}$
Since number of favoravle cases can not be greater than total number of cases,
Probability $< 1$.
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MCQ 31 Mark
A coin is tosses $1000$ times, if the probability of getting a tail is $\frac{3}{8},$ how many times head is obtained?
  • A
    $525$
  • B
    $375$
  • ✓
    $625$
  • D
    $725$
Answer
Correct option: C.
$625$
Probability of getting a tail $=\frac{3}{8}$
$\Rightarrow $ Probability of geeting a head $=1-\frac{3}{8}=\frac{5}{8}$
Also,
Probability of getting a head $=\frac{\text{No.of heads obtained}}{\text{Total no. of trials}}$
$\Rightarrow\ \frac{5}{8}=\frac{\text{No. of heads obtained}}{1000}$
$\Rightarrow $ No. of heads obtainted $=\frac{5}{8}\times1000=625$
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MCQ 41 Mark
Which of the following cannot be the probability of an event?
  • A
    $\frac{1}{3}$
  • B
    $\frac{3}{5}$
  • ✓
    $\frac{5}{3}$
  • D
    $1$
Answer
Correct option: C.
$\frac{5}{3}$
The probability of an event always lies between $0$ and $1$.
Since $\frac{5}{3}>1,$ it cannot be the probability of an event.
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MCQ 51 Mark
The probability of an impossible event is:
  • A
    $1$
  • ✓
    $0$
  • C
    Less than $0$
  • D
    Greater than $1$
Answer
Correct option: B.
$0$
The probability of an impossible event is always zero since the chances of occurring of that event is zero.
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MCQ 61 Mark
The probability of a certain event is:
  • A
    $0$
  • ✓
    $1$
  • C
    Greater than $1$
  • D
    Less than $0$
Answer
Correct option: B.
$1$
The chance of occuring of an certain event is always 100%.
Probability $=\frac{\text{No. of favorable cases}}{\text{Total no. of cases}}$
Thus, for a certain event,
Number of favorable cases = Total number of cases
$\Rightarrow $ Probability $= 1$
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MCQ 71 Mark
Two coins are tassed simultaneously. The probability of geeting atmost one head is:
  • A
    $\frac{1}{4}$
  • ✓
    $\frac{3}{4}$
  • C
    $\frac{1}{2}$
  • D
    $\frac{5}{4}$
Answer
Correct option: B.
$\frac{3}{4}$
If two coins are tossed simultaneously, then possible cases are $HH, TH, HT, TT.$
Total number of cases $= 4$
Number of favorable cases (atmost one head) $= (HT, TH, TT) = 3$
Now,
Probability of getting atmost one head $=\frac{3}{4}$
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MCQ 81 Mark
In a football match, Ronaldo makes $4$ goals from $10$ penalty kicks. The probability of converting a penalty kick into a goal by Ronaldo, is:
  • A
    $\frac{1}{4}$
  • B
    $\frac{1}{6}$
  • C
    $\frac{1}{3}$
  • ✓
    $\frac{2}{5}$
Answer
Correct option: D.
$\frac{2}{5}$
Probability that Ronaldo makes a goal
$=\frac{\text{Number of goal made in all kicks}}{\text{Total number of kicks}}$
$=\frac{4}{10}=\frac{2}{5}$
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MCQ 91 Mark
A bag contains $50$ coins and each coin is marked from $51$ to $100$. One coin is picked at random. The probability that the number on the coin is not a prime number, is:
  • A
    $\frac{1}{5}$
  • B
    $\frac{3}{5}$
  • C
    $\frac{2}{5}$
  • ✓
    $\frac{4}{5}$
Answer
Correct option: D.
$\frac{4}{5}$
Prime numbers from $51$ to $100$:
$53, 59, 61, 67, 71, 73, 79, 83, 89, 97$
$\Rightarrow $ Number of prime numbers $= 10$
$\Rightarrow $ Numver of non-prime numbers $= 50 - 10 = 40$
Total numbers $= 50$
Thus, probability of getting no-prime number $=\frac{40}{50}=\frac{4}{5}$
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MCQ 101 Mark
The percentage of attendance of different classes in a year in a school is given below:
Class
$X$
$IX$
$VIII$
$VII$
$VI$
$V$
Attendance
$30$
$62$
$85$
$92$
$76$
$55$
What is the probability that the class attendance is more than $75 \%$?
  • A
    $\frac{1}{6}$
  • B
    $\frac{1}{3}$
  • C
    $\frac{5}{6}$
  • ✓
    $\frac{1}{2}$
Answer
Correct option: D.
$\frac{1}{2}$
Total number of classes $= 6$
Number of classes having attendance $> 75 \% = VIII, VII, VI = 3$
$\Rightarrow $ Required probability $=\frac{3}{6}=\frac{1}{2}$
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M.C.Q - MATHS STD 9 Questions - Vidyadip