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Subsection 3.2.3 Probability of Simple Events
Activity 3.2.3 .
\({\color{black} \textbf{Work in groups}}\)
Kanyama rolls a fair six-sided die. What is the probability of Kanyama rolling a
\(4\)
Identify the Sample Space.
Identify the Favorable Outcomes
Apply the Probability Formula
Discuss and compare answers
\({\color{black} \textbf{Key Takeaway}}\)
A simple event is an event that consists of only one outcome in the sample space.
The probability of a simple event is given using the formula
\begin{gather*}
\textbf{P(E)} = \frac{\textbf{Number of favorable outcomes}}{\textbf{Number of Outcomes}}
\end{gather*}
where;
\(\textbf{P(E)}\) is the probability of event
\(\textbf{E}\)
Favorable outcomes refer to the specific event we are interested in
Total outcomes refer to all possible outcomes in the sample space
Example 3.2.7 .
A bag contains 5 red balls and 3 blue balls. If one ball is picked at random, what is the probability that it is red?
Solution .
Total number of balls
\(\textbf{ = 5 + 3 = 8}\)
Number of red balls
\(\textbf{ = 5}\)
Given a bag with
\(5\) red balls and
\(3\) blue balls, the possible outcomes when picking one ball are
\(\textbf{S = {Red,Blue}}\)
Total outcomes
\(\textbf{ = 5 + 3 = 8}\)
Probability of drawing a red ball is given by:
\(\textbf{P(Red)}=\frac{\textbf{Number of favorable outcomes}}{\textbf{Number of Outcomes}} = \frac{5}{8}=\textbf{0.625}\)
the probability of picking a red ball is
\(0.625\) or
\(62.5\%\)
Example 3.2.8 .
A teacher at Sironga Secondary school randomly selects a student from a class of 30 students. If there are 12 girls and 18 boys in the class, what is the probability that the selected student is a girl?
Solution .
Sample Space is
\begin{gather*}
\textbf{S = {Girl, Boy}}
\end{gather*}
The number of favorable outcomes that is choosing a girl =
\(\textbf{12}\)
Now, Applying our formula gives
\begin{gather*}
\textbf{P(Girl)}=\frac{\textbf{Number of girls}}{\textbf{Total number of students}}
\end{gather*}
\begin{gather*}
= \frac{12}{30}
\end{gather*}
\begin{gather*}
=\textbf{0.4}
\end{gather*}
The probability of selecting a girl is
\(0.4\) or
\(40\%\)
Exercises Exercises
1. What is the probability of selecting the letter ’a’ from the name "Mukabwa"?
2. A deck of standard playing cards has 52 cards. What is the probability of drawing the 5 of Hearts?
3. A bag has 3 yellow marbles, 5 black marbles, and 2 white marbles. What is the probability of selecting a white marble?
4. A month is selected at random from a year. What is the probability that it is June?
5. A coin is tossed. What is the probability of getting tails?
6. A box contains tickets numbered from 1 to 10. What is the probability of drawing a ticket with the number 7?
7. A class has 25 students, and one student is chosen at random. What is the probability that a specific student is chosen?
8. What is the probability of selecting the letter "e" from the word "elephant"?
Checkpoint 3.2.9 .
Checkpoint 3.2.10 .
