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## NCERT Class 10 Maths Textbook Chapter 15 With Answer Book PDF Free Download

### Chapter 15: Probability

#### 15.2 Probability — A Theoretical Approach

Let us consider the following situation :

Suppose a coin is tossed at random. We know, in advance, that the coin can only land in one of two possible ways —

either head up or tail up (we dismiss the possibility of its ‘landing’ on its edge, which may be possible, for example, if it falls on sand). We can reasonably assume that each outcome, head or tail, is as likely to occur as the other. We refer to this by saying that the outcomes head and tail, are equally likely.

For another example of equally likely outcomes, suppose we throw a die once. For us, a die will always mean a fair die. What are the possible outcomes?

They are 1, 2, 3, 4, 5, 6. Each number has the same possibility of showing up. So the equally likely outcomes of throwing a die are 1, 2, 3, 4, 5, and 6. Are the outcomes of every experiment equally likely?

Let us see. Suppose that a bag contains 4 red balls and 1 blue ball, and you draw a ball without looking into the bag. What are the outcomes?

Are the outcomes — a red ball and a blue ball equally likely? Since there are 4 red balls and only one blue ball, you would agree that you are more likely to get a red ball than a blue ball. So, the outcomes (a red ball or a blue ball) are not equally likely.

However, the outcome of drawing a ball of any color from the bag is equally likely.

So, all experiments do not necessarily have equally likely outcomes. However, in this chapter, from now on, we will assume that all the experiments have equally likely outcomes.

Author | NCERT |

Language | English |

No. of Pages | 18 |

PDF Size | 1316 KB |

Category | Mathematics |

Source/ Credits | ncert.nic.in |

### NCERT Solutions Class 10 Maths Chapter 15 Probability

**1. Complete the following statements:**

(i) Probability of an event E + Probability of the event ‘not E’ = ___________.

(ii) The probability of an event that cannot happen is __________. Such an event is called ________.

(iii) The probability of an event that is certain to happen is _________. Such an event is called _________.

(iv) The sum of the probabilities of all the elementary events of an experiment is __________.

(v) The probability of an event is greater than or equal to ___ and less than or equal to __________.

**Solution:**

(i) Probability of an event E + Probability of the event ‘not E’ = **1**.

(ii) The probability of an event that cannot happen is **0**. Such an event is called **an impossible event**.

(iii) The probability of an event that is certain to happen is **1**. Such an event is called **a sure or certain event**.

(iv) The sum of the probabilities of all the elementary events of an experiment is **1**.

(v) The probability of an event is greater than or equal to **0** and less than or equal to **1**.

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

(i) A driver attempts to start a car. The car starts or does not start.

(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.

(iii) A trial is made to Solution: a true-false question. The solution is right or wrong.

(iv) A baby is born. It is a boy or a girl.

**Solution:**

(i) This statement does not have equally likely outcomes as the car may or may not start depending upon various factors like fuel, etc.

(ii) Even this statement does not have equally likely outcomes as the player may shoot or miss the shot.

(iii) This statement has equally likely outcomes as it is known that the solution is either right or wrong.

(iv) This statement also has equally likely outcomes as it is known that the newly born baby can either be a boy or a girl.

**3. 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?**

**Solution:**

Tossing a coin is a fair way of deciding because the number of possible outcomes is only 2 i.e. either head or tail. Since these two outcomes are equally likely outcomes, tossing is unpredictable and is considered to be completely unbiased.

**4. Which of the following cannot be the probability of an event?**

**(A) 2/3 (B) -1.5 (C) 15% (D) 0.7**

**Solution:**

The probability of any event (E) always lies between 0 and 1 i.e. 0 ≤ P(E) ≤ 1. So, from the above options, option (B) -1.5 cannot be the probability of an event.

**5. If P(E) = 0.05, what is the probability of ‘not E’?**

**Solution:**

We know that,

P(E)+P(not E) = 1

It is given that, P(E) = 0.05

So, P(not E) = 1-P(E)

Or, P(not E) = 1-0.05

∴ P(not E) = 0.95

NCERT Class 10 Maths Textbook Chapter 15 With Answer Book PDF Free Download