Probability

Probability

Theoretical And Experimental

What is Probability?

Probability is a branch of mathematics that involves the study of how likely an event is to occur

Probability of Simple Event

• When a coin is tossed, how likely is it to get a head? If the coin is fair, it is equally likely to get a head or tail. There is a 50% chance of getting a head. Or we say the probability of the event that a head occurs is 1 out of 2 or In general, any subset of a sample space is called an event.

   

• Sample space of equally likely outcomes, the probability of an event, denoted as (E), is calculated on the basis of favorable outcomes and the number of possible outcomes.

  
  

• With this in mind, the answer to our question would be: ½ 

What is Experimental probability

Experimental probability refers to the probability of an event occurring when an experiment was conducted and determined on the basis of the results of an experiment repeated many times

Example :

toss a coin 5 times, a head recorded 3 times while the tail recorded 2 times

-        P_(Head) = 3/5

-        P_(Tail) = 2/5

what is Theoretical Probability

Theoretical probability is determined by noting all the possible outcomes theoretically, determining how likely the given outcome is and determined on the basis of reasoning

Example :

A Coin is tossed.

-        P(Head) = 1/2

-        P(Tail) = 1/2

To better understand the Probability of simple event, theoretical and experimental let have a quiz

Probabilities can be solved theoretically in which each event is assumed to be equally likely. Look carefully at the given set then match column A with column B. Your answers will help you understand the concept on the probability of an event.

Multiple Choice

Given: Set R = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

The probability of having 10?

• 1/ 12

• 1/6

• 1/4

• 1/2

• 0

Multiple Choice

Given: Set R = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

The probability of having 13?

• 1/ 12

• 1/6

• 1/4

• 1/2

• 0

Multiple Choice

Given: Set R = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

The probability of having odd number?

• 1/ 12

• 1/6

• 1/4

• 1/2

• 0

Multiple Choice

Given: Set R = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

The probability of having odd number divisible by 3?

• 1/ 12

• 1/6

• 1/4

• 1/3

• 1/2

Multiple Choice

Given: Set R = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

The probability of having a two number who's sum is equal to 12?

• 5/ 12

• 5/6

• 1/4

• 1/3

• 1/2

Open Ended

A bowl of flower seeds contains 5 petunia seeds and 15 begonia seeds. Riley calculated the probability that a randomly selected seed is a petunia seed as . Describe and correct Riley’s error

Open Ended

There are 20 seventh graders and 15 eighth graders in a club. A club president will be chosen at random.

a. Compare the probabilities of choosing a seventh grader or an eighth grader.

b. If a student from one grade is more likely to be chosen than a student from the other, is the method unfair? Explain.