Intro to probability - 1
1 like155 views
This document introduces key concepts in probability through examples. It discusses what probability is, possible outcomes, events, equally likely events vs. not equally likely events, certain and impossible events, the complement of an event, the probability line, mutually exclusive vs. not mutually exclusive events. Examples used include a spinner with colors, coin tossing, dice rolling, and drawing balls from a jar. Probability is defined as the number of ways an event can happen divided by the total number of possible outcomes.
![We could find the probability of the inverse of the statement.
What that is meant ?
Probability Line
In every scenario,
probability of anything will rest in between 0 to 1.
Probability of blue can be written as,
p(blue) =
OR
p(Blue) = 1 - p(not blue) [ p(not blue) = ]](https://image.slidesharecdn.com/introtoprobability-190331165249/85/Intro-to-probability-1-7-320.jpg)
Intro to probability - 1
- 1. Intro to probability - 1 Contents - 1 . What is probability ? 2. Possible outcomes 3. Event 4. Equally likely events 5. Not equally likely events 6. Certain and impossible events 7. Complement of a event 8. Probability line 9. Mutually Exclusive events 10.Not Mutually exclusive events
- 2. ** What is probability ? "probability is the likelihood or chance of occuring an event". Suppose we have a spinner like this, Lets assume it spins both ways. the question is , what is the chance of getting red portion selected by the marker when we spin. (Though its totally random.Mathematics can't assure it that when we are gonna get red or some other colors.) What mathematics can do is, can derive an idea of getting a color from all those possibilities. and here in a single spin there is 4 possibilty. those are called possible outcomes. so , In this scenario here is 4 possible outcomes. ** Possible Outcomes
- 3. ** Event Event is actually a single or multiple outcome from all possible outcomes.Depend on what we are looking for. What is the possibility of getting red from the spinner scenario ?? This getting red is an event what we are interested in. Lets denote this , Probability of getting red is = How many ways this event can happen ?? Here is 4 slice in this spinner with 4 different colors. And only 1 is red. So the number of ways happening that event is 1. ** Defining Porbability Probability of some event can written as, Number of possible outcomes Number of ways that event may happen some event
- 4. ** Equally Likely Events Lets talk about a new scenario,Tossing a coin. Here is 2 possible outcomes. Head or tail. p(Head) = p(Tail) = the probability of getting head or tail is same.This kind if events are called equally likely events. One more example, Rolling a 6 sided dice Here is 6 possible outcomes.
- 5. p(1) = p(2) = p(3) = p(4) = p(5) = p(6) = So probability of getting any outcomes from a dice is same.Those are alose equally likely events. ** Not equally likely events Suppose , a glass jar contain 6 green ball , 5 red ball, 8 blue ball and 3 yellow balls. Number of balls = 6 + 5 + 8 + 3 = 22. p(Green) = p(Red) = p(Blue) = p(Yellow) = Possibility of those outcomes are not equal to each other.This is a not equally likely event.
- 6. Certain and impossible events What is the probability off picking a purple ball from the jar. the number of purble ball is 0. so , p(Purple) = 0 its a impossible event. Whats is the probability of picking a ball which is either green or red or blue or yellow ?? Since , All the balls are of these colors. p(Green / Red / Blue / Yellow) = 22 / 22 = 1 its a certain event that you cant get rid of. ** Complement of an event Suppose we have a spinner like this, Lets reconsider the spinner scenario again. What if we ask you to find the probability of getting blue out of all possible outcomes ?
- 7. We could find the probability of the inverse of the statement. What that is meant ? Probability Line In every scenario, probability of anything will rest in between 0 to 1. Probability of blue can be written as, p(blue) = OR p(Blue) = 1 - p(not blue) [ p(not blue) = ]
- 8. It can be written as, ** Mutually Exclusive Event Reconsider the coin tossing, outcomes - A : Head B : Tail Is it really possible to get A and B together ? no,its impossible. Those events are called Mutually exclusive events. ** Not Mutually Exclusive Event Rolling a Dice - Expected outcomes A : an even number between 1 to 6 B : a number greater than 2
- 9. Here is 2 possible outcomes those are validate both A and B together.So those A and are not mutually exclusive events.