What is Probability ?, Types of Probabiliy
What is Probability?
Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0. An event with a probability of 1 can be considered a certainty: for example, the probability of a coin toss resulting in either "heads" or "tails" is 1, because there are no other options, assuming the coin lands flat. An event with a probability of .5 can be considered to have equal odds of occurring or not occurring: for example, the probability of a coin toss resulting in "heads" is .5 because the toss is equally as likely to result in "tails." An event with a probability of 0 can be considered an impossibility: for example, the probability that the coin will land (flat) without either side facing up is 0 because either "heads" or "tails" must be facing up. A little paradoxical, probability theory applies precise calculations to quantify uncertain measures of random events.⬇Types Of Probability⬇
- Classical Probability:
Classical Probability is a statistical concept that measures the likelihood of something happening. Classical probability is the statistical concept that measures the likelihood of something happening, but in a classic sense, it also means that every statistical experiment will contain elements that are equally likely to happen.
The typical example of classical probability would be a fair dice roll because it is equally probable that you will land on any of the 6 numbers on the die: 1, 2, 3, 4, 5, or 6.
Another example of classical probability would be a coin toss. There is an equal probability that your toss will yield a heads or tails result.
Example 1:
Example 2:
If we wanted to determine the probability of getting an even number when rolling a die, 3 would be the number of favorable outcomes because there are 3 even numbers on a die (and obviously 3 odd numbers). The number of possible outcomes would be 6 because there are 6 numbers on a die. Therefore, the probability of getting an even number when rolling a die is 3/6, or 1/2 when you simplify it.
Example 2:
Take a look at these 7 markers in the colors of red, green, brown, blue, black, yellow, and purple. If you placed them into a Ziploc bag and drew one out while blindfolded, there is an equal chance in a probability that you would choose each one, so this is an example of classical probability.
- Experimental Probability:
Experimental probability is the ratio of the number of times an outcome occurs to the total number of times the activity is performed.
Experimental probability (EP) is a probability based on data collected from repeated trials.
Let n represent the number of times an experiment is done.
Let p represent the number of times an event occurred while performing this experiment n times.
Let n represent the number of times an experiment is done.
Let p represent the number of times an event occurred while performing this experiment n times.
Example ⬎
A manufacturer makes 25,000 cell phones every month. After inspecting 500 phones, the manufacturer found that 10 phones are defective. What is the probability that you will buy a phone that is defective? Predict how many phones will be defective next month.
EP = 10/500 = 0.020.02 = 1/500 = 2%
The probability that you will buy a defective phone is 2%
Number of defective phones next month = 2% × 25000
Number of defective phones next month = 0.02 × 25000
Number of defective phones next month = 500
Experimental probability is performed when authorities want to know how the public feels about a matter. Since it is not possible to ask every single person in the country, they may conduct a survey by asking a sample of the entire population. This is called population sampling.
- Theoretical Probability:
Theoretical Probability.Theoretical Probability: probability based on reasoning written as a ratio of the number of favorable outcomes to the number of possible outcomes.
Example ⬎
Sample question: What is the theoretical probability of rolling a 4 or a 7 with a set of two dice?If this question asked you the empirical probability, you could set up an experiment. For example, you could roll the die a hundred times, record the results and state the probability. But as this question is asking you the theoretical probability, you need to use a formula or set up a sample space. As there is no single formula for calculating die rolling probabilities, set up a sample space.
Step 1: Set up a sample space. In other words, write out all of the possible “events” that can happen. In this case, the events are the numbers that come up after the dice are rolled. For two dice, the probabilities are:
[1][1], [1][2], [1][3], [1][4], [1][5], [1][6],[2][1], [2][2], [2][3], [2][4],[2][5], [2][6],[3][1], [3][2], [3][3], [3][4], [3][5], [3][6],[4][1], [4][2], [4][3], [4][4], [4][5], [4][6],[5][1], [5][2], [5][3], [5][4], [5][5], [5][6],[6][1], [6][2], [6][3], [6][4], [6][5], [6][6].
I’ve bolded the rolls that result in a total of 7.
Step 2: Figure out the probability. The entire sample space is made up of 36 possible rolls. There are 9 rolls that result in a 7, so the answer is:
9/36 = .25.
Step 2: Figure out the probability. The entire sample space is made up of 36 possible rolls. There are 9 rolls that result in a 7, so the answer is:
9/36 = .25.
- Subjective Probability:
- You think you have an 80% chance of your best friend calling today because her car broke down yesterday and she’ll probably need a ride.
- You think you have a 50/50 chance of getting the job you applied for because the other applicant is also very qualified.
- You’re taking your dog to the vet today, and based on past experience you’re pretty confident you’ll need over $100 for the bill
