Experimental and Theoretical Probability Worksheet

Experimental and theoretical are two main ways by which the probability of an event can be found. Probability is a fundamental concept in mathematics that quantifies the likelihood of different outcomes in uncertain situations. Understanding probability is crucial for making informed decisions in various fields such as science, engineering, finance, and everyday life. This detailed introduction will explore both types, their differences, and their importance.

What is Experimental and Theoretical Probability?

Experimental probability is determined by conducting experiments or simulations and observing the outcomes. It is calculated by dividing the number of times an event occurs by the total number of trials. Experimental probability is particularly useful when the theoretical probability is difficult to calculate or when real-world data is available. It can be expressed as:

P(E) = (Number of Times Event Occurs)\(Total Number of Trials)

For example, if you flip a coin 100 times and get heads 55 times, the experimental probability of getting heads is:

P(Heads) = {55}/{100} = 0.55

Theoretical probability is based on the assumption that all outcomes in a given situation are equally likely. It involves calculating the probability of an event by analyzing the possible outcomes and using mathematical principles. Theoretical probability is often used in situations where all possible outcomes are known, and it can be expressed as:

P(E) = {Number of Favorable Outcomes}/{Total Number of Possible Outcomes}

For example, when flipping a fair coin, the theoretical probability of getting heads is:

P(Heads) = {1/2}

Important Formulas

In Experimental Probability

• P(Event) = (Number of Times Event Occurs)\(Total Number of Trials)

In Theoretical Probability

• P(Event) = {Number of Favorable Outcomes}/{Total Number of Possible Outcomes}

Worksheet: Experimental and Theoretical probability

Q1. A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the experimental probability of getting a blue marble.

Q2. A bag contains 8 red marbles, 9 pink marbles and 1 yellow marbles. Find the experimental probability of getting a blue marble.

Q3. The number of pancakes prepared by Fredrick per day this week is in the order of 4, 7, 6, 9, 5, 9, and 5. What will you say if I ask you to give me a credible estimate of the likelihood that Fredrick will make less than 6 pancakes the next day based on this data?

Q4. The following set of data shows the number of messages that Mike received recently from 6 of his friends. 4, 3, 2, 1, 6, 8. Based on this, find the probability that Mike will receive less than 2 messages next time.

Q5. A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the experimental probability of getting a yellow marble.

Q6. A bag contains 8 marbles. You randomly draw a marble from the bag, record its color, so replace it. The table shows the results after 12 draws. The amount of green marbles within the bag is?

Q7. A bag contains 5 red balls, 3 green balls, and 2 blue balls. John draws a ball from the bag, records the color, and then puts it back into the bag. He repeats this process 100 times and records the following results:

• Red: 48 times
• Green: 32 times
• Blue: 20 times

Find:

1. What is the experimental probability of drawing a red ball?
2. What is the experimental probability of drawing a green ball?
3. What is the experimental probability of drawing a blue ball?

Practice problems Experimental and Theoretical Probability

Problem 1: The table shows the results of spinning a penny 62 times. What’s the probability of spinning heads?

• 23 - Heads
• 39 - Tails

Solution:

Heads were spun 23 times in a total of 23 + 39 = 62 spins.

P (heads) = \frac{23}{69}

= 0.37 or 37.09 %

Problem 2: You randomly choose one among seven letters. What’s the theoretical probability of randomly choosing an X?

Solution:

P (x) = {Number of favorable outcomes}/{Total number of possible outcomes}

= 17 = 14.28%

Problem3 : A coin is tossed 10 times. It’s recorded that heads occurred 6 times and tails occurred 4 times.

Solution:

• P(heads) ={6/10} = 3/5
• P(tails) = {4/10} = 2/5

Problem 4: Find the probability when a coin is tossed.

Solution:

When a coin is tossed there are two chances first is head and the other one is tails. So we have to find the probability of both.

• P(heads) = {1}/{2}
• P(tails) = {1}/{2}

Problem 5: What is the probability of tossing a variety cube and having it come up as a two or a three?

Solution:

First, find the full number of outcomes Outcomes: 1, 2, 3, 4, 5, and 6

Total Outcomes = 6

Next, find the quantity of favorable outcomes.

Favorable Outcomes: Getting a 2 or a 3 = 2

Then, find the ratio of favorable outcomes to total outcomes.

P (Event) = {Number of favorable outcomes}/{Total number of possible outcomes}

P (2 or 3) = 2/6 = 1/3

The theoretical probability of rolling a 2 or a 3 on a variety of cube is 1:3.

Problem 6: A bag contains 25 marbles. You randomly draw a marble from the bag, record its color, so replace it. The table shows the results after 11 draws. The probability of finding red marbles and green marbel is?

Solution:

Total Marbles = 1 + 3 + 5 + 2

P (E) = {Number of times event occurs}/{Total number of trials}

P (Red) = 5/11

P(Green) = 3/11

Read More:

• Probability Theory
• Practice Problem on Probability

Frequently Asked Questions

Can Experimental Probability of an Event be Negative Number?

No, since the quantity of trials during which the event can happen can not be negative and also the total number of trials is usually positive.

Tossing a coin comes under which type of probability ?Theoretical ProbabilityOr Experimental Probability.

Tossing a coin comes under Theoretical Probability.

What do you mean by Zero Probability?

When the chance of occurrence of an event is zero then it is called as zero probability.

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• Mathematics