MCQ(1M)

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 $\text{\{HH, TH, HT, TT\}}.$
Total number of cases $= 4$
Number of favorable cases $($atmost one head$) = (\text{HT, TH, TT}) = 3$
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 $> 75\% = \text{VIII, VII, VI} = 3$
$\Rightarrow$ Required probability $=\frac{3}{6}=\frac{1}{2}$

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