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Probability Guide Book
Transcript of Probability Guide Book
Probability Guide Book
Probability is a number from 0 to 1 that describes how likely an event is to occur. Probability can be shown as P(event). The probability of an event can be classified as impossible, unlikely, as likely as not, likely, or certain. Impossible means that there is a 0% chance that the event will occur. On the other hand, certain means that there is a 100% chance that the event will occur. As likely as not would mean that the chances of the event occurring are 50%. One example of probability would be: Nell always does her homework. What is the probability that Nell has done her homework? The probability would be certain because Nell ALWAYS does her homework leading to the conclusion that she did do her math homework. Another example would be the weather forecast shows that there is a 70% chance of rain. The probability of it raining would be 70% or .7. I solved this equation by doing P(rain)= 70% or .7. The probabilities must always add to one, so the probability of no rain is P(no rain)= 1-.7=.3 or 30%. Sample space are all the possible outcomes of an experiment. For example, if you roll a dice with six sides, the sample space or all of the possible outcomes would be 1,2,3,4,5, and 6 because there are six possible numbers that the dice could land on.
Experimental probability is the ratio of the number of times an event occurs to the total number of trials, or times that the experiment is performed. Experimental probability is different from theoretical probability because the ratio for theoretical probability is the number of equally likely outcomes in an event to the total number of possible outcomes. One example of experimental probability would be: Katie was looking at the trees she passed in the forest. She saw 29 oak, 9 pine, and 12 apple trees. What is the probability that the next tree Katie sees is an apple tree? The probability would be .24 or 24%. I found this out by making the ratio 12(number of apple)/50(total number of trees). Then I made this number into a percent by multiplying the numerator and the denominator by 2 to get the denominator to 100. When the numerator was multiplied by 2, it turned into 24 making the probability be 24/100 or 24%. This could also be shown as a fraction or decimal. Another example would be: Alexandra has a bag of marbles. She has pulled 15 green, 10 blue, 13 red, and 12 yellow. What is the probability that the next marble Alexandra pulls out of the bag is green? The probability would 30%. I found this out by using the same steps shown in the example above.
Theoretical probability is the ratio of the number of equally likely outcomes in an event to the total number of possible outcomes. Theoretical probability is different to experimental probability because the ratio for experimental probability is the number of times an event occurs over the total number of trials. An example of theoretical probability would be: Sally has 12 red, white, blue and purple rocks in a bag. What it the probability that Sally will pick a red rock out of the bag? The probability would be 1/4. I found this out by using the formula 12(number of equally likely outcomes in an event/48(total number of outcomes. I then simplified the ratio making my answer 1/4. Another example would be: Ryan tosses a penny and then it lands on the table. What it the probability that the penny lands on heads? The probability would be 1/2. I found this out by using the same formula as used above.
The Counting Principle
The Counting Principle states that if one event had "m" possible outcomes and a second event had "n" possible outcomes after the first event has been chosen then there are m*n total possible outcomes for the two events. An example of this would be: A zip code company is assigned a new zip codes that they need to issue. The zip code has 7 digits. All zip codes are equally likely. Find the number of possible combinations for the 7 digit zip codes. The answer is 10,000,000. I found this out by looking at how many digits there are(7), and the number choices for the digits(10 because there are 10 different number to choose from). Then, because there are 7 digits, I did 10 to the 7th power.
Independent and Dependent Events
An independent event is an event that does not affect the outcome of another event. On the contrary, a dependent event does affect the outcome of another event. An example of an independent event would be flipping two coins and having one land on heads and the other tails because the two coins did not influence which side the other would land on. An example of a dependent event would be drawing a card from a deck of cards and then drawing another card without replacing the first card. This is dependent because since the card is not put back, it decreases the amount of cards you could draw on your next draw.
A tree diagram is a branching diagram that shows all the possible outcomes or combinations of an event. An example of a tree diagram would be: Bob and Susie both like chocolate milk, white milk, chocolate chip cookies, and oatmeal cookies. What are all of the possible combinations of cookies and milk that they can eat? The answer would be six possible combinations because the tree diagram show below gives six different combinations of cookies and milk.
Another example would be: A social security company needs to think of social security numbers for their clients. The social security numbers must have nine digits. How many different combinations can this company use? There are 1,000,000,000 combinations. I found this it by using the same formula as shown in the first example for The Counting Principle.
Examples for Independent Events
Another example for an independent event would be Sam has a bag of marbles. He draws one from the bag, replaces it, and then he draws another. This is independent because Sam replaces the marble making it eligible to be chosen again along with all of the other marbles that did not get chosen. Another example would be Ally chooses a pen from a section of the store and then she chooses a candy from a different section. This is independent because choosing a pen and then choosing a candy have no affect on each other.
Examples for Dependent Events
An example of a dependent event would be Alexis and Grace go to the store. Alexis chooses a binder and then Grace chooses a binder. This is dependent because Grace does not have as many binders to choose from because Alexis already chose a binder before Grace. Another example would be Mark chooses something to eat from the fridge and then his brother, Jay, chooses something to eat from the fridge. This is dependent because Jay doesn't have as many options to choose from because his brother already took something from the fridge.
My sources for this project were sections 10-1, 10-2, 10-4, 10-5, and 10-8 in my Holt Georgia Mathematics Course 3 Textbook. Also, I used my notes in my INB notebook.