- What is Probability
- |
- Why we need Probability and what is the use of it
- |
- Terms related to Probability
- |
- Empirical Probability
- |
- Theoretical Probability
- |

This page contains probability class 10 ncert solutions from qiestions 1 to 8 on page number 308 Exercise 15.1

Qiestion 1

Complete the following statements:

- Probability of an event E + Probability of the event ‘not E’ =…………….
- The probability of an event that cannot happen is ……. Such an event is called ……..
- The probability of an event that is certain to happen is………. . Such an event is called …….
- The sum of the probabilities of all the elementary events of an experiment is ………..
- The probability of an event is greater than or equal to ……….and less than or equal to ………

Solution

We know that

The event $\bar A$, representing ‘not A’, is called the complement of the event A. We also say that $\bar A$ and A are complementary events. Also**P(A) +P($\bar A$)=1****So answer is 1**- The probability of an event (U) which is impossible to occur is 0. Such an event is called an
**impossible event****P(U)=0** - The probability of an event ( X) which is sure (or certain) to occur is 1. Such an event is called a
**sure event or a certain event****P(X)=1** - An event having only one outcome of the experiment is called an elementary event.
“

**The sum of the probabilities of all the elementary events of an experiment is 1.”**i.e. If we three elementary event A,B,C in the experiment ,then

**P(A)+P(B) +P(C)=1** - Probability of any event can be as

$$0 \le P(E) \le 1$$

**Question 2**

Which of the following experiments have equally likely outcomes? Explain.

- A driver attempts to start a car. The car starts or does not start.
- A player attempts to shoot a basketball. She/he shoots or misses the shot.
- A trial is made to answer a true-false question. The answer is right or wrong.
- A baby is born. It is a boy or a girl

**Solution**

- Not equally likely
- Not equally likely
- Equally likely as both have equal possibility
- Equally likely as the baby born has equal possibility of boy or girl

**Question 3**

Why is toss ing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

**Solution**

Since the possibility of getting head and tail are equally likely. It will be unbiased and unpredictable

**Question 4**

Which of the following cannot be the probability of the event

- 2/3
- -1.5
- 15%
- .7

**Solution**

(b) as probability cannot be negative

**Question 5**

If P(E) = 0.05, what is the probability of ‘Not E’?

**Solution**

The event $\bar A$, representing ‘not A’, is called the complement of the event A. We also say that $\bar A$ and A are complementary events. Also

**P(A) +P(****$\bar A$)=1**

Here P(E) =.05

So P**(****Not E)=1 – P(E)**

** =1-.05=.95**

**Question 6**

A bag contains lemon colored candies. Malini takes out one candy without looking into the bag. What is the probability that she takes out

- An orange colored candy
- An lemon colored candy

**Solution**

- So probability of getting orange candy is zero
- Since she will always get lemon candy, probability is 1

**Question 7**

It is given that in a group of 3 students, the probability of 2 students not having the same birthday is .992. What is the probability that 2 students have the same birthday?

**Solution**

Let A be the event 2 students not having the same birthday

And B be the event 2 students having same birthday

These both the events are complimentary so

P(A)+P(B)=1

P(B)=1-.992=.008

**Question 8**

A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is

- Red
- No red

**Solution:**

Total number of balls in the bad n(B)=5+3=8

No of ball which are red =3

- Let A be event of getting red ball Probability of getting red ball P(A)= No of red balls/Total number of balls= 3/8
- Let B be the event of getting non red ball P(B) =No of black balls/ Total number of balls=5/8

Go Back to Class 10 Maths Home page Go Back to Class 10 Science Home page

- Mathematics (Class 10) by RD Sharma
- NCERT Solutions - Mathematics Class 10
- NCERT Exemplar Mathematics Problems - Solutions (Class 10)
- Board + IIT - JEE Foundation Mathematics (Class 10) by disha experts
- Mathematics Foundation Course for JEE/AIPMT/Olympiad Class : 10 (by mtg)
- Board + PMT/ IIT Foundation for JEE Main / Advanced: Science & Mathematics, Class - 10
- Class Companion - Class 10 Mathematics