ProbabilitiesProbabilitiesProbabilitiesProbabilities

Introduction• Human life is full of uncertainties.

In our day to day life very often we make guess & use statements like :”possibility of a particular party to win this election is more “,”Most probably it will rain to-day “.

Analizing some real life situations

• When we toss a coin ,it cannot be predicted whether there will be head or tail.

• *When we throw a 6faces die ,it cannot be predicted whether there will be no. 1,2,3,4,5or6.

• *It is possible that I may not go for a picnic.

• *Probably it will rain tomorrow.

• In the probability ,we numerically measure the degree of certainty or uncertainty in terms of nos. lying between 0 & 1

• *An event for an experiment is the collection of some outcomes of the experiment.

Probability an experimental

approach..• Galileo ,an Italian mathematician was the 1st

man to attempt at a quantitative measure of probability while dealing with some probs. Related to the theory of dice in gambling .

*But the 1st foundation of the mathematical theory of probability was laid in 1654 by 2 French mathematicians ,Blaire Pascal & Pierre de Fermat while solving a no. of probs. Posed by French gambler Chevalier-de Mere to Pascal. Both Pascal & Fermat solve the probs. Independantly . This work was the beginning of Probability theory.

1) Experiments ..

• A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble? a green marble? a blue marble? a yellow marble?

• Outcome• The possible outcomes of this

experiment are red, green, blue and yellow

P(red) No. of ways to choose redTotal no. of marbles

6/22 3/11

P(green) No. of ways to choose greenTotal no. of marbles

5/22

P(blue) No. of ways to choose blueTotal no. of marbles

8/22 4/11

P(yellow) No. of ways to choose yellowTotal no.of marbles

3/22

2) Experiment…

A single 6-sided die is rolled. What is the probability of each outcome? What is the probability of rolling an even number? of rolling an odd number?

The possible outcomes of this experiment are 1, 2, 3, 4, 5 and 6.

Outcome

P(1) number of ways to roll 1 total number of sides

1/6

P(2) number of ways to roll2 total number of sides

1/6

P(3) number of ways to roll3 total number of sides

1/6

P(4) number of ways to roll4 total number of sides

1/6

P(5) number of ways to roll5 total number of sides

1/6

P(6) number of ways to roll6 total number of sides

1/6

P(even) ways to roll an even no. total number of sides

3/6 = 1/2

P(odd) ways to roll an odd no. total number of sides

3/6 = 1/2

Symbolically, the probability of an event

can be written as :

P(E) = n(E)/n(S)

Probs. ????? To solve……

• A spinner has 4 equal sectors colored yellow, blue, green and red. What are the chances of landing on blue after spinning the spinner? What are the chances of landing on red

Ans….

• The chances of landing on blue are 1 in 4, or one fourth. The chances of landing on red are 1 in 4, or one fourth.

Some more….• A dice is thrown once . Find

the probability of getting a prime number ????

• Ans..• 1/2

……• If a coin is tossed then the

probability of getting head is ???

• Ans…• 1/2