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THEORETICAL PROBABILITY

Theoretical Probability

Definition Of Theoretical Probability

It is the likeliness of an event happening based on all the possible outcomes. The ratio for the probability of an event 'P' occurring is P (event) = number of favorable outcomes divided by number of possible outcomes.

Examples of Theoretical Probability

From the letters A, E, I, O, U the theoretical probability of selecting the letter E is 1/5

Video Examples: Finding Theoretical Probability

 

 

Solved Example on Theoretical Probability

Ques: A coin is tossed on a standard 8X 8 chessboard. What is the theoretical probability that the coin lands on a black square?

Choices:

A. 0.5
B. 0.25
C. 0.42
D. 0.6
Correct answer: A

Solution:

Step 1: Theoretical probability = number of favorable outcomes / number of possible outcomes.
Step 2: The probability of the coin lands on the black square is 32.
Step 3: Total number of outcomes = 64.
Step 4: P (event) = 32/64
Step 5: = 1/2 = 0.5
Step 6: The theoretical probability that the coin lands on a black square is 0.5.

Quick Summary

  • Theoretical probability calculates the likelihood of an event before it occurs.
  • It's based on reasoning and not on experimental data.
  • The probability value always ranges between 0 and 1.
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]

🍎 Teacher Insights

Use real-world examples like dice rolls, coin flips, and card draws to illustrate theoretical probability. Emphasize the importance of identifying all possible outcomes.

🎓 Prerequisites

  • Basic arithmetic
  • Understanding of fractions

Check Your Knowledge

Q1: What is the theoretical probability of rolling a 4 on a standard six-sided die?

Q2: A bag contains 3 red marbles and 5 blue marbles. What is the theoretical probability of picking a red marble?

Frequently Asked Questions

Q: What is the difference between theoretical and experimental probability?
A: Theoretical probability is what we expect to happen, while experimental probability is what actually happens after conducting an experiment.

Q: Can theoretical probability be greater than 1?
A: No, theoretical probability always lies between 0 and 1, inclusive.

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