Probability

Experiment: Any activity or trial performed is an experiment.

e.g. 1) Tossing of coin

2) Rolling of dice

3) Falling of rain

·      Outcomes: The results of the activity are called outcomes.

e. g. out comes for above experiments are

1) Head, Tail

2) $\text{1, 2, 3, 4, 5, 6}$

3) It will rain, It will not rain.

·      Probability of happening of event

$\text{P}\left(\text{E}\right)\text{ = }\frac{\text{no}\text{.of trials in which event happened}}{\text{Total no}\text{.of trials}}$

If total no. of trials = n

If no. of times event $\text{E}$ occurred $\text{= m}$

Then $\text{P}\left(\text{E}\right)\text{ = }\frac{\text{m}}{\text{n}}$

·      Probability always lies between $\text{0}$ and v.

·      $\text{0}\le \text{p}\left(\text{E}\right)\le \text{1}$

·      If ${\text{E}}_{\text{1}}{\text{, E}}_{\text{2}}{\text{, E}}_{\text{3}}\text{, }\mathrm{...}{\text{, E}}_{\text{n}}$ are the possible outcomes of an experiments, then sum of probabilities of each event is $\text{1}$.

i.e $\text{P}\left({\text{E}}_{\text{1}}\right)\text{ + P}\left({\text{E}}_{\text{2}}\right)\text{ + P}\left({\text{E}}_{\text{3}}\right)\text{ +}\mathrm{...}\text{+P}\left({\text{E}}_{\text{n}}\right)\text{ = 1}$

e.g.

For an experiment rolling a dice

The possible out comes = Numbers - $\text{- 1, 2, 3, 4, 5, 6}$ So let event ${\text{E}}_{\text{1}}\text{=}$ getting $\text{1}$ on die, ${\text{E}}_2\text{=}$ getting 2 on die and so on.

Then $\text{P}\left({\text{E}}_{\text{1}}\right)\text{ + P}\left({\text{E}}_{\text{2}}\right)\text{ + P}\left({\text{E}}_{\text{3}}\right)\text{ +}\mathrm{...}\text{+P}\left({\text{E}}_{\text{6}}\right)\text{ = 1}$