Theoretical Probability

Topic Content:

This is the computation of the likelihood of an event occurring based on logic and mathematical reasoning without actually performing an experiment.

Examples of theoretical probability include flipping a fair coin and getting heads or tails, rolling a six-sided die and getting a certain number.

Mathematically;

Theoretical prob = \( \frac{No\:of\:favourable\:outcomes}{Total\:no\:of\:possible\: outcomes} \)

Example 6.3.1:

A bag contains 8 red balls, 4 black balls and 9 white balls. Find the probability of:

(a) picking a red ball
(b) a white ball
(c) not picking a black ball

Solution:

Total number of balls: 8 + 4 + 9 = 21

(a) P_{(red ball)} = \( \frac{8}{21} \)

(b) P_{(white ball)} = \( \frac{9}{21} \\ = \frac{3}{7}\)

(c) P_{(not black ball)} = \( \scriptsize 1 \: -\: P_{(black)} \\ \scriptsize = 1 \: -\: \normalsize \frac{4}{21} \\ = \frac{21\:-\:4}{21}\\ = \frac{17}{21} \)

Example 6.3.2:

40 discs, marked with numbers 1 to 40 inclusive are put in a bag. Find the probability that the number on the disc drawn from the