1. Probabilities

2. 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 “.

3. 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.

4. 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.

5. 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.

6. 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

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

10. Symbolically, the probability of an event can be written as : P(E) = n(E)/n(S)

11. 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

12. 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. Ans….

13. Some more…. • A dice is thrown once . Find the probability of getting a prime number ???? • Ans.. • 1/2

14. …… • If a coin is tossed then the probability of getting head is ??? • Ans… • 1/2