Ideas

Ideas

Ideas

**Probability Guide Book**

By: Nell Kropp/Blue Class

By: Nell Kropp/Blue Class

Probability

The probability of an event is a number from 0% to 100%. This number tells you how likely the event is to happen. Probability can be measured by using the words impossible, unlikely, as likely as not, likely, and certain. Impossible means that there is a 0% chance that it will happen. On the other hand, certain means that there is a 100% chance that the event will occur. Additionally, as likely as not means that there is a 50% chance that the event will occur. Sample space is the set of all possible outcomes of an experiment. For example, you have 2 coins and a spinner with 4 sections. You could have 16 different outcomes because there are 2 heads and 2 tails. Then, you add 2(heads)+2(tails) to get 4 and multiply 4(sections)*4(heads and tails) to get 16 different possible outcomes.

Examples

Ex #1= There is a 50% chance of rain today. What is the chance that it will rain today? (impossible,unlikely,as likely as not, likely, or certain)

This is as likely as not. I figured this out because 50/100 is equal to 50%, and it simplifies to 1/2 meaning that there is an equal chance that it will rain or not rain.

Ex #2= You have a spinner with four sections labeled 1-4. What is the probability that the spinner will land on the section labeled 4? (impossible, unlikely, as likely as not, likely, or certain)

This is unlikely because there is a 1/4 chance which is less than 1/2.

Experimental Probability

Experimental probability is the ratio of the total number of times an event occurs to the total number of trials. Experimental probability is different from theoretical probability because in experimental probability, you are actually performing an experiment. In Theoretical probability, you are doing the number of ways the event can occur divided by the total number of likely outcomes.

Ex #1= I have a spinner with 4 sections labeled 1-4. I spin the spinner 10 times and my spinner lands on 1 two times, 2 four times, 3 one time, and 4 four times. What is the experimental probability that the dice will land on three? The experimental probability of the spinner landing on 3 is 1/10 times.

Ex #2= I role a standard dice with 6 sides labeled 1-6 twenty times. The dice lands on 1 eight times, 2 four times, 3 and 4 zero times, 5 six times, and 6 two times. What is the experimental probability that you will roll a one? The experimental probability that you will role a one is 2/5 times. I figured this out by writing the amount of times 1 was rolled divided by the total number of rolls (20). This came out to 8/20 which simplified to 4/5.

Independent and Dependent Events

There is a difference between independent and dependent events. Independent events are events that do not effect the probability of other events. For example, a coin landing on heads on one toss and tails the next toss is an independent event. On the other hand, dependent events are events that do effect the probability of other events. For example, when you draw a card from a deck labeled 1-20 and keep the card, it is a dependent event.

Theoretical probability is used to estimate probabilities by making certain assumptions about an experiment. Theoretical probability is different from experimental probability because in experimental probability, you are actually performing an experiment. Theoretical probability is more like a guess. You can find experimental probability by dividing the number of ways the event can occur by the total number of equally likely outcomes. For example, Ms. Howson randomly selects one name out of a hat to represent her class in the Math Bee. There are 30 students in her class. There are 10 boys and 20 girls in her class. What is the theoretical probability that she will pick a boy's name? There is a 1/3 chance that a boy's name will get pulled because there are 10 boys in her class out of 30 total students. This simplifies to 1/3. Here is another example. What is the theoretical probability of randomly choosing a blue jelly bean out of a bag with 5 blue beans, 10 red beans, 2 yellow beans, and 3 pink beans? The theoretical probability of picking a blue jelly bean is 1/4 because there are 5 blue beans out of 20 possible beans. This is 5/20 which simplifies to 1/4.

Tree Diagrams and Counting Principle

A tree diagram is a branching diagram that shows all the possible outcomes of an event. The Fundamental Counting Principle is if there are "m" ways to choose a first item and "n" ways to choose a second item after the first item is chosen, then there are "m" * "n" ways to choose all the items. For example, find the number of possible five digit zip codes by using the Fundamental Counting Principal. There are 100,000 possible five digit zip codes. I found this because each digit has a 0-9 chance. Then I multiplied 10*10*10*10*10. You can also see that there are five zeroes and add those zeroes behind the one. Additionally, what is the probability of not having a 1 on your license tag in Georgia? Georgia license tags have 4 numbers. The numbers will range from 0-9. There is a .6561 probability of not having a license tag with the number 1. I found this by multiplying 9*9*9*9 (6,561). Then, I divided that by the total possible combinations, 10,000. Finally, I got .6561.

Example...

Examples...

Ex #3= You pick a red card from a stack of red, blue, and green cards and keep the card. This is a dependent event because you will now have more of a chance of picking any of the other cards.

Ex #4= You have a spinner labeled 1-4 and you roll a 4. Then, you cross out the number four. This is a dependent event because now you will only have three numbers that the spinner can land on.

Independent

Example...

Independent

Ex #2= Abby rolls a 5 on a dice labeled 1-6. On her second roll, she roles a 1. This is an independent event because her rolling a 5 on the first roll has no effect on the second roll.

Ex #1= On Sunday, it rains. Then, two weeks later on Sunday it is Sunny. This is an independent event because the weather on the first Sunday listed has no effect on the weather on the Sunday two weeks later.

Example...