Mathematics Lab Activity-22 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 - 22

Objective

To write the sample space, when a coin is tossed once, two times, three times, four times ….. and so on.

Material Required

One rupee coin, pen/pencil, paper, plastic circular discs marked with Head (H) and Tail (T). 

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)Toss a coin once. It has two outcomes – Head or Tail as shown in fig. 21.1

Fig. 21.1

2) Toss a coin twice. It has four out comes as shown in fig. 21.2

Figure 21.2

3) Toss a coin three times. It has eight outcomes as shown in fig. 21.3

Figure 21.3

4) Toss a coin four times. It has 16 outcomes as shown in fig. 21.4

Figure. 21.4

5) Repeat this process five times, 6 times ….. so on , and write their sample space..

Observations

1) If a coin is tossed once, then the sample space is  S = {H, T}

Number of elements in S = 2 = 2¹.

2) If a coin is tossed twice, then the sample space is  S = {HH, HT, TH, TT}

Number of elements in S = 4 = 2².

3) If a coin is tossed thrice, then the sample space is  S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Number of elements in S = 8 = 2³.

4) If a coin is tossed thrice, then the sample space is  S = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, THHT, THTH, TTHH, HTTH, HTTT, THTT, TTHT, TTTH, TTTT}

Number of elements in S = 16 = 2⁴   and so on.

Result

Number of elements in the sample space, when a

1) Coin is tossed once = 2¹ = 2

2) Coin is tossed twice = 2² = 4

3) Coin is tossed 3 times = 2³ = 8

4) Coin is tossed 4 times = 2⁴ = 16   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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