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

This page contains NCERT solutions for Class 10 Maths Chapter 15: probability for Exercise 15.1

- 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 ………

- 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

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

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

- 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

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

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

Which of the following cannot be the probability of the event

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

(b) as probability cannot be negative

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

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

Here P(E) =.05

So P

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

The bag does not contain any orange candy

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

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?

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

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

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

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