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## NCERT Class 11 Maths Textbook Chapter 16 With Answer PDF Free Download

### Chapter 16: Probability

#### 16.1 Introduction

In earlier classes, we studied the concept of probability as a measure of uncertainty of various

phenomena.

We have obtained the probability of getting an even number in throwing a die as 3/6 i.e., 1/2 Here the total possible outcomes are 1,2,3,4,5 and 6 (six in number).

The outcomes in favor of the event of ‘getting an even number’ are 2,4,6 (i.e., three in number).

In general, to obtain the probability of an event, we find the ratio of the number of outcomes favorable to the event, to the total number of equally likely outcomes. This theory of probability is known as the classical theory of probability.

In Class IX, we learned to find the probability on the basis of observations and collected data. This is called the statistical approach of probability.

Both theories have some serious difficulties. For instance, these theories can not be applied to the activities/experiments which have an infinite number of outcomes.

In classical theory we assume all the outcomes to be equally likely. Recall that the outcomes are called equally likely when we have no reason to believe that one is more likely to occur than the other.

In other words, we assume that all outcomes have an equal chance (probability) to occur.

Thus, to define probability, we used equally likely or equally probable outcomes.

This is logically not a correct definition. Thus, another theory of probability was developed by A.N. Kolmogorov, a Russian mathematician, in 1933.

Author | NCERT |

Language | English |

No. of Pages | 29 |

PDF Size | 1978 KB |

Category | Mathematics |

Source/Credits | ncert.nic.in |

### NCERT Solutions Class 11 Maths Chapter 16 Probability

**1. A coin is tossed three times.**

**Solution:-**

Since either coin can turn up Head (H) or Tail (T), the possible outcomes may be

So, when 1 coin is tossed once the sample space = 2

Then,

Coin is tossed 3 times the sample space = 2^{3} = 8

Thus, the sample space is S = {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}

**2. A die is thrown two times.**

**Solution:-**

Let us assume that 1, 2, 3, 4, 5 and 6 are the possible outcomes when the die is thrown.

Then, the total number of sample spaces = (6 × 6)

= 36

Thus, the sample space is

S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3)(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

**3. A coin is tossed four times.**

**Solution:-**

Since either coin can turn up Head (H) or Tail (T), these are the possible outcomes.

So, when 1 coin is tossed once the sample space = 2

Then,

Coin is tossed 3 times the sample space = 2^{4} = 16

Thus, the sample space is S = {HHHH, THHH, HTHH, HHTH, HHHT, TTTT, HTTT, THTT, TTHT, TTTH, TTHH, HHTT, THTH, HTHT, THHT, HTTH}

**4. A coin is tossed and a die is thrown.**

**Solution:-**

Since either coin can turn up Head (H) or Tail (T), these are the possible outcomes.

Let us assume that 1, 2, 3, 4, 5 and 6 are the possible numbers that come when the die is thrown.

Then, total number of space = (2 × 6) = 12

Thus, the sample space is,

S={(H,1),(H,2),(H,3),(H,4),(H,5),(H,6),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}

**5. A coin is tossed and then a die is rolled only in the case ahead is shown on the coin.**

**Solution:-**

Since either coin can turn up Head (H) or Tail (T), these are the possible outcomes.

Let us assume that 1, 2, 3, 4, 5 and 6 are the possible numbers that come when the die is thrown.

When head in encountered,

Then, number of space = (1 × 6) = 6

Sample Space S_{H}= {H1, H2, H3, H4, H5, H6}

Now, tail is encountered, Sample space S_{T}= {T}

Therefore the total sample space S = {H1, H2, H3, H4, H5, H6, T}

**6. 2 boys and 2 girls are in Room X, and 1 boy and 3 girls are in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.**

**Solution:-**

From the question, it is given that,

2 boys and 2 girls are in Room X

1 boy and 3 girls in Room Y

Let us assume b1, b2 and g1, g2 be 2 boys and 2 girls are in Room X.

And also assume b3 and g3, g4, and g5 be 1 boy and 3 girls in Room Y.

The problem is solved by dividing it into two cases

Case 1: Room X is selected

Sample Space S_{x }= {(X,b1),(X,b2),(X,g1),(X,g2)}

Case 2: Room Y is selected

Sample Space S_{y} ={(Y,b3),(Y,g3),(Y,g4),(Y,g5)}

The overall sample space

S={(X,b1),(X,b2),(X,g1),(X,g2),(Y,b3),(Y,g3),(Y,g4),(Y,g5)}

**7. One die of red color**, one of white color** and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face are noted. Describe the sample space.**

**Solution:-**

Let us assume that 1, 2, 3, 4, 5, and 6 are the possible numbers that come when the die is thrown.

And also assume die of red color be ‘R’, die of white colour be ‘W’, die of blue colour be ‘B’.

So, the total number of sample space = (6 × 3) = 18

The sample space of the event is

S={(R,1),(R,2),(R,3),(R,4),(R,5),(R,6),(W,1),(W,2),(W,3),(W,4),(W,5),(W,6) (B,1),(B,2),(B,3),(B,4),(B,5),(B,6)}

NCERT Class 11 Maths Textbook Chapter 16 With Answer Book PDF Free Download