Mathematics Lab Activity-21 Class XI

Mathematics Laboratory Activities on Probability for class XI students Non-Medical. These activities are according to the CBSE syllabus

Chapter - 16 probability

Activity - 21

Objective

To write the sample space, when a dice is rolled once, twice, thrice....

Material Required

A die, plastic discs marked with 1, 2, 3, 4, 5, 6, paper pencil/pen etc.

Theory

Probability of an event

If E is an event then :- P(E) + P(notE) = 1
Probability of an event is greater than, equal to 0 but is less than, equal to 1. This is also be called as the range of Probability

Impossible Event:-
An event which never occur is called impossible event.
P(Impossible Event) = 0

Sure Event :
An even which happens for sure is called sure event. Sure event is also be called as the certain event.
P(Sure Event or Certain Event) = 1

Equally likely events:-
If every event of the sample space has equal possibility to happen, then the events are called equally likely events. (e.g. Tossing a coin)

Procedure

1) Throw a dice once. The number on its top will be 1, 2, 3, 4, 5, 6.
2. Make a tree diagram showing its six branches with numbers 1, 2, 3, 4, 5, or 6 as shown in fig. 20.1

Fig. 20.1

3.) Write the sample space of these outcomes.

4) Throw a die twice. It can fall in any of the 36 ways as shown in figure 20.2 by the tree diagram.

Figure 20.2

5) Repeat the experiment by throwing the die 3 times, 4 times and so on…  and write the sample space of the outcomes in each time.

Observations

1) If a die is thrown once, then the sample space is :

S = {1, 2, 3, 4, 5, 6}.                                                                       

Number of elements in S  = 6 = 6¹

2) If a die is thrown twice, the sample space is :

Number of elements is S = 36 = 6².

3.) If the die is thrown twice, then the number of elements in the sample space will be = 6³ = 216 and so on.

Result

If a die is thrown once then number of elements in the sample space is = 6¹.

If a die is thrown twice then number of elements in the sample space is = 6².

If a die is thrown thrice then number of elements in the sample space is = 6³.

If a die is thrown 4 times then number of elements in the sample space is = 6⁴.

………… and so on. 

Applications

Sample space of an element can be used to determine the probabilities of different events associated with that sample space.

VIVA – VOICE

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