PROBABILITY ( LECTURE 3)

LESSON 3 PROBABILITY

DEAR STUDENTS
WELCOME TO THE CLASS  !!

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General Instructions

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Today's learning outcomes are:

I will be able to:

1 recall basic definitions and formula of probability.

2. comprehend the sample space for tossing of coin(s)

3. calculate probability related to tossing of coin(s).

Let's calculate probability of events associated with experiment of TOSSING COIN(S)

Firstly,It is important to understand the sample space with respect to these experiments.

Click on the link 
So, by now you would have got a fair idea about the sample space.

As you have seen in the video , we will be considering three experiments related to tossing coins

NOTE DOWN
Experiment 1: Tossing a coin
Sample space={H,T}

Total possible outcomes =2¹ =2


Experiment 2: Tossing 2 coins simultaneously / Tossing 2 coins one after the other

Total possible outcomes =2² =4

Experiment 3: Tossing 3 coins simultaneously / Tossing 3 coins one after the other

Total possible outcomes =2³ =8

So,if 4 coins are tossed then what will be  total possible outcomes ?

Try to create a sample space for 4 coins.

. HAVE YOU EVER THOUGHT

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?

☛IN TOSSING OF A COIN ,THE OUTCOMES GETTING HEAD OR TAIL ARE EQUALLY LIKELY.THE RESULT OF TOSS IS COMPLETELY UNPREDICTABLE.

LET'S do Q23 of EX 15.2

23. A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Sample space ={ HHH,HTT,THT,TTH,HHT,THH,HTH,TTT}

Total possible outcomes = 8

No. of favourable outcomes =8- 2 =6  (EXCLUDE   HHH,TTT from sample  space)

P(losing the game)  = 6/8=3/4

Solved Eg 9

 Harpreet tosses two different coins simultaneously (say, one is of   Re 1 and other of Rs  2). What is the probability that she gets at least one head?

Sample space={HH,HT,TH,TT}

CLICK ON THE LINK TO  understand it better

So,What do you mean by atleast 1 head??

Atleast 1 head means more than equal to 1 head. So, here you have to take following :

1 head - HT,TH

2heads - HH   

So, total no . of possible outcomes are 4

total no . of favourable  outcomes are  3

P(getting atleast  1 head )=   3…./…4.

In the same question, calculate probability of  getting atmost 1 head

Atmost 1 head means - less than or  equal to 1 head

So, we will take 0 head- TT

                           1head-HT ,TH

                           

The required probability is...…………….

Question. In a game, the entry fee is of Rs. 5. The game consists of a tossing a coin 3 times. If one or two heads show, Shweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. otherwise she will lose. For tossing a coin three times, find the probability that she

(i) loses the entry fee.

(ii) gets double entry fee.

(iii) just gets her entry fee.

Ans.  total no . of possible outcomes are = 8
Sample space = { HHH,HTT,THT,TTH,HHT,THH,HTH,TTT}

(I) Shweta  loses the entry fee. if she gets no head means TTT
 So, P( she loses the entry fee.)  =1/8


(ii) Shweta gets double entry fee. means she gets all 3 heads HHH

So, P( she gets double entry fee.)  = 1/8


(iii) Shweta just gets her entry fee means she gets 1 or 2 

heads HTT,THT,TTH,HHT,THH,HTH,

So, required probability is 6/8 =3/4

Ex 15.1 Q10, Q25(i)

Some more questions:

1.Find the probability of getting one head if a coin is thrown twice

2.  A coin is tossed 3 times. List the possible outcomes. Find the probability of getting (i) all heads (ii) atleast 2 heads 

Boys , during the second period try to solve all the example qns from NCERT.

Today's class ends here!!

See you all tomorrow for next class.