MATH 8-Basic-Concept-of-Probability.pptx

math 8

1. Illustrating an Experiment, Outcome, Sample Space and Event Basic Concept of Probability

2. probability Probability is a branch of mathematics that measures or estimates how likely an event will happen. Events cannot be predicted with total certainty. "How likely are they to happen?“ it is known as the chance or possibility that something will occur or happen.

3. in the picture below, this is what they call the probability line. When they say zero probability , it only means that it is impossible to happen.

4. Zero probability EXAMPLE: There is a zero probability that it will snow in the Philippines . If the probability is 0.25 or 25%, it is unlikely to happen. Yes, it will happen, but only sometimes. And, if the probability is 50% or even chance, if it is 75% probability, or four in five chance, it means it is likely to happen. And lastly , if the probability is certain, then it is a 100% probability.

5. PROBABILITY I t is often shown as a decimal or fraction. EXAMPLE: When you toss a coin, there are only 2 results; it is either "HEAD" or "TAIL". For example, the probability of getting a "head" when tossing a coin It can be shown as: As a decimal : 0.5 As a fraction: ½ As a percentage: 50% ; and sometimes as ratio: 1:2 / 1in 2.

6. EXPERIMENT An experiment is an activity involving chances that can have different results. It is a process that, when performed, results in exactly one of many observations. Activities such as tossing or flipping a coin , rolling a die , or picking a card from a standard deck of cards without looking could be repeated over and over again and have well defined results .

7. EXPERIMENT EXAMPLE You need to get a number 6 in rolling a die to win in the game of snake and ladder. What is the experiment in this situation ? The experiment is getting a number 6 by rolling a die.

8. EXPERIMENT EXAMPLE Jen and Jan are playing cards. Jan needs to draw a card numbered 5 to win the game from a well- shuffled deck of 5, 8, 9, 2, and 7 cards and place it face down on the table. Jane, what is the experiment in this situation? The experiment is drawing a card.

9. OUTCOME When we say outcomes, these are the results of experiments. EXAMPLE: N umber 1 situation, rolling a die once is an example of experiment where you can have a possible outcomes and those are 1, 2, 3, 4, 5, and 6. There are 6 possible outcomes because as you can see there are 6 faces in a die.

10. OUTCOME EXAMPLE: N umber 2 , Jen and Jan are playing cards. Jan needs to draw a card numbered 5 to win the game from a well- shuffled numbered 5, 8, 9, 2, and 7 cards and place it face down on the table. What are the possible outcomes? The possible outcomes in the situation are cards 5, 8, 9, 2, 7.

11. SAMPLE SPACE Sample Space is the set of all possible outcomes of an experiment and is denoted by S . Sample space is just the same as outcome, where you have to list all the possible outcomes, but the only difference is that sample space is written within brackets.

12. SAMPLE SPACE FOR EXAMPLE: Number 1 situation is that you need to get a number 6 in rolling a die to win in the game of snake and ladder. The sample space is 1, 2, 3, 4, 5, 6.

13. SAMPLE SPACE FOR EXAMPLE: Jen and Jan are playing cards. Jan needs to draw a card numbered 5 to win the game from a well-shuffled deck of 5, 8, 9, 2, and 7 cards and place it face down on the table. The sample space is {5, 8, 9, 2, 7}.

14. SAMPLE POINT A sample point is an individual outcome in the sample space. It is one of the possible outcomes. If sample space is the list of all possible outcome, the sample point is talking about individual outcome in the sample space of an experiment.

15. SAMPLE POINT FOR EXAMPLE if the situation is drawing a card from a deck of 52 cards, is King can be considered as a sample point? N o , because there are four different kings in the deck of cards, which are also considered four different sample points.

16. EVENT An event is a set of some elements or outcomes of an experiment. It is a subset of a sample space. It is not necessary to be the actual outcome of the experiment . EXAMPLE number 1: you need to get a number 6 in rolling a die to win in the game of snake and ladder. In rolling a die, there are 6 possible outcomes, and if the condition is that you get only an even number, what will the event be in that experiment? The events in that experiment are{2, 4, 6}.

17. EVENT EXAMPLE Jen and Jan are playing cards. Jan needs to draw a card numbered 5 to win the game from a well-shuffled deck of 5, 8, 9, 2, and 7 cards and placed face down on the table. The events in that experiment are {2, 5, 7 } .

18. THANKYOU FOR LISTENING! Hope you understand the lesson