Chapter 25 Probability R.D. Sharma Solutions for Class 9th MCQ's
Multiple Choice Questions1. 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
Solution
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 by P(A) and is given by
P(A) = m/n
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 0/n = 0.
Hence, the correct option is (b).
2. The probability of a certain event is
(a) 0
(b) 1
(c) greater than 1
(d) less than 0
Solution
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 by P(A) and is given by
P(A) = m/n
Hence the correct option is (b).
3. The probability an event of a trial is
(a) 1
(b) 0
(c) less than 1
(d) more than 1
Solution
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 by P(A) and is given by
P(A) = m/n
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 n/n = 1 , 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).
4. Which of the following cannot be the probability of an event ?
(a) 1/3
(b) 3/5
(c) 5/3
(d) 1
Solution
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 by P(A) and is given by
P(A) = m/n
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 n/n = 1, 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).
5. Two coins are tossed simultaneously. The probability of getting atmost one head is
(a) 1/4
(b) 3/4
(c) 1/2
(d) 1/4
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 by P(A) and is given by
P(A) = m/n
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 n/n = 1, 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).
5. Two coins are tossed simultaneously. The probability of getting atmost one head is
(a) 1/4
(b) 3/4
(c) 1/2
(d) 1/4
Solution
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 by P(A) and is given by
P(A) = m/n
Therefore, we have
P(A) = 3/4
So, the correct choice is b .
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
Solution
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 by P(A) and is given by
P(A) = m/n
Therefore, we have P(A) = x/1000
But, it is given that P(A) = 3/8. So, we have
x/1000 = 3/8
⇒ 8x = 3000
⇒ x = 3000/8
⇒ x = 375
Hence, a tail is obtanined 375 times.
Consequently, a head is obtained 1000-375 = 625 times.
So, the correct choice is (c).
7. A dice is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 are given below:
The probability of getting a prime number is
(a) 1/3
(b) 2/3
(c) 49/60
(d) 39/125
Solution
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 by P(A) and is given by
P(A) = m/n
Therefore, we have
P(A) = 3/4
So, the correct choice is b .
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
Solution
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 by P(A) and is given by
P(A) = m/n
Therefore, we have P(A) = x/1000
But, it is given that P(A) = 3/8. So, we have
x/1000 = 3/8
⇒ 8x = 3000
⇒ x = 3000/8
⇒ x = 375
Hence, a tail is obtanined 375 times.
Consequently, a head is obtained 1000-375 = 625 times.
So, the correct choice is (c).
7. A dice is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 are given below:
The probability of getting a prime number is
(a) 1/3
(b) 2/3
(c) 49/60
(d) 39/125
Solution
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 30+120+50 = 200.
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 by P(A) and is given by
P(A) = m/n
therefore, we have
P(A) = 200/600 =1/3
So. the correct choice is (A)
8. The percentage of attendance of different classes in a year in a school is given below:
Let A be the event of getting a prime number (2, 3 and5).
The number of times A happens is 30+120+50 = 200.
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 by P(A) and is given by
P(A) = m/n
therefore, we have
P(A) = 200/600 =1/3
So. the correct choice is (A)
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 |
(a) 1/6
(b) 1/3
(c) 5/6
(d) 1/2
Solution
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 by P(A) and is given by
P(A) = m/n
Therefore , we have
P(A) = 3/6 = 1/2
So, the correct choice is (d).
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) 1/5
(b) 3/5
(c) 2/5
(d) 4/5
Solution
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 50-10 = 40 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 by P(A) and is given by
P(A) = m/n
Therefore, we have
P(A) = 40/50 = 4/5
So, the correct choice is (d).
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) 1/4
(b) 1/6
(c) 1/3
(d) 2/5
Solution
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 by P(A) and is given by
P(A) = m/n
Therefore, we have
P(A) = 4/10 = 2/5
So, the correct choice is (d) .