RD Sharma 2020 solution class 9 chapter 25 Probabilty MCQS

MCQS

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Question 1:

Mark the correct alternative in each of the following:
The probability of an impossible event is

(a) 1
(b) 0
(c) less than 0
(d) greater than 1
 

Answer 1:

We have to find the probability of an impossible event.
Note that the number of occurrence of an impossible event is 0. This is the reason that’s why it is called impossible event.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Note that n is a positive integer, it can’t be zero. So, whatever may be the value of n, the probability of an impossible event is.
Hence the correct option is (b).

Question 2:

The probability of a certain event is

(a) 0
(b) 1
(c) greater than 1
(d) less than 0

Answer 2:

We have to find the probability of a certain event.
Note that the number of occurrence of an impossible event is same as the total number of trials. When we repeat the experiment, every times it occurs. This is the reason that’s why it is called certain event.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Note that n is a positive integer, it can’t be zero. So, the probability of an impossible event is.
Hence the correct option is (b).

Question 3:

The probability an event of a trial is

(a) 1
(b) 0
(c) less than 1
(d) more than 1

Answer 3:

Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Note that m is always less than or equal to n and n is a positive integers, it can’t be zero. But, m is a non negative integer. So, the maximum value of probability of an event is, which is the probability of a certain event and the minimum value of it is 0, which is the probability of an impossible event. For any other events the value is in between 0 and 1.
Hence the correct option is (c).

Question 4:

Which of the following cannot be the probability of an event?

(a) $\frac{1}{3}$

(b) $\frac{3}{5}$

(c) $\frac{5}{3}$

(d) 1

Answer 4:

Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Note that m is always less than or equal to n and n is a positive integers, it can’t be zero. But, m is a non negative integer. So, the maximum value of probability of an event is, which is the probability of a certain event and the minimum value of it is 0, which is the probability of an impossible event. For any other events the value is in between 0 and 1.
All the options except (c) satisfy the above criteria’s.
Hence the correct option is (c).

Question 5:

Two coins are tossed simultaneously. The probability of getting atmost one head is

(a) $\frac{1}{4}$

(b) $\frac{3}{4}$

(c) $\frac{1}{2}$

(d) $\frac{1}{4}$

Answer 5:

The random experiment is tossing two coins simultaneously.
All the possible outcomes are HH, HT, TH, and TT.
Let A be the event of getting at most one head.
The number of times A happens is 3.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have

So, the correct choice is (b).

Question 6:

A coin is tossed 1000 times, if the probability of getting a tail is 3/8, how many times head is obtained?
(a) 525

(b) 375

(c) 625

(d) 725

Answer 6:

The total number of trials is 1000. Let x be the number of times a tail occurs.
Let A be the event of getting a tail.
The number of times A happens is x.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have.
But, it is given that. So, we have


Hence a tail is obtained 375 times.
Consequently, a head is obtainedtimes.
So, the correct choice is (c).

Question 7:

A dice is rolled 600 times and the occurrence 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 getting a prime number is

(a) $\frac{1}{3}$

(b) $\frac{2}{3}$

(c) $\frac{49}{60}$

(d) $\frac{39}{125}$

Answer 7:

The total number of trials is 600.
Let A be the event of getting a prime number (2, 3 and5).
The number of times A happens is.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have

So, the correct choice is (a).

Question 8:

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) $\frac{5}{6}$

(d) $\frac{1}{2}$

Answer 8:

The total number of trials is 6.
Let A be the event that the attendance of a class is more than 75%.
The number of times A happens is 3 (for classes’ VIII, VII and VI).
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have

So, the correct choice is (d).

Question 9:

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) $\frac{2}{5}$

(d) $\frac{4}{5}$

Answer 9:

The total number of trials is 50.
Let A be the event that the number on the picked coin is not a prime.
The prime’s lies in between 51 and 100 are 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. They are 10 in numbers. Therefore the numbers lies between 51 and 100 and which are not primes are in numbers.
So, the number of times A happens is 40.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have

So, the correct choice is (d).

Question 10:

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) $\frac{1}{3}$

(d) $\frac{2}{5}$

Answer 10:

The total number of trials is 10.
Let A be the event that Ronaldo makes a goal in a penalty kick.
The number of times A happens is 4.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have

So, the correct choice is (d).

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Question 11:

Mark the correct alternative in each of the following:

Three biased coins were tossed 800 times simultaneously. The outcomes are given in the following table :

Outcome   :     No head     One Head      Two Head

Frequency :     120             280                    x

If the probability of occurrence of two heads is thrice that of all heads,  then the value of x.
(a) 150
(b) 240
(c) 300
(d) 340

Answer 11:

Three biased coins are tossed 800 times.

∴ Total number of trials = 800

Let E be the event of occurrence of two heads and F be the event of occurrence of all heads.

∴ Probability of occurrence of two heads = P(E) = $\frac{\mathrm{Number} \mathrm{of} \mathrm{trials} \mathrm{of} \mathrm{occurrence} \mathrm{of} \mathrm{two} \mathrm{heads}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials}}=\frac{x}{800}$      .....(1)

Now,

Number of trials of occurrence of all heads (or three heads)

= Total number of trials − Number of trials of occurrence of no head − Number of trials of occurrence of one head − Number of trials of occurrence of two heads

= 800 − 120 − 280 − x

= 400 − x

∴ Probability of occurrence of all heads = P(F) = $\frac{\mathrm{Number} \mathrm{of} \mathrm{trials} \mathrm{of} \mathrm{occurrence} \mathrm{of} \mathrm{all} \mathrm{heads}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials}}=\frac{400-x}{800}$      .....(2)

It is given that,

Probability of occurrence of two heads = 3 × Probability of occurrence of all heads

$\therefore \frac{x}{800}=3\times \left(\frac{400-x}{800}\right)$              [From (1) and (2)]

$\Rightarrow x=1200-3x$

$\Rightarrow 4x=1200$

$\Rightarrow x=\frac{1200}{4}=300$

Thus, the value of x is 300.

Hence, the correct answer is option (c).

Question 12:

Mark the correct alternative in each of the following:

An unbiased dice was rolled 800 times simultaneously. The frequencies of the various outcomes are given in the table below :

Outcome   :     1        2      3      4    5      6  

Frequency :     150  200  100  75  125  150 
When the dice is rolled, the probability of getting a number which is a perfect square is

$$\begin{gathered} \left(\mathrm{a}\right) \frac{9}{32} \\ \left(\mathrm{b}\right) \frac{11}{32} \\ \left(\mathrm{c}\right) \frac{13}{32} \\ \left(\mathrm{d}\right) \frac{15}{32} \end{gathered}$$

Answer 12:

It is given that an unbiased dice was rolled 800 times.

∴ Total number of trials = 800

Let E be the event of getting a number on the dice which is a perfect square.

Now, 1 and 4 are perfect squares among the outcomes 1, 2, 3, 4, 5 and 6.

∴ Number of trials of getting a number which is perfect square on the dice

= Frequency of getting 1 or 4 on the dice

= 150 + 75

= 225

So, P(Getting a number which is perfect square) = P(E) = $\frac{\mathrm{Number} \mathrm{of} \mathrm{trials} \mathrm{of} \mathrm{getting} \mathrm{a} \mathrm{number} \mathrm{which} \mathrm{is} \mathrm{perfect} \mathrm{square}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials}}=\frac{225}{800}=\frac{9}{32}$

Thus, the probability of getting a number which is a perfect square is $\frac{9}{32}$.

Hence, the correct answer is option (a).