8A - Introduction to probability
8A - Content video: Introduction to probability
This video covers the theory and several examples relating to the introduction to probability. To help get started have a think about the riddle below...
■ Alan and Bob are playing a game. Each of them pays $30 to start the game (a total of $60 in the jackpot). Alan and Bob have an equal chance to win; that is, the probability of Alan winning is 0.5 and the probability of Bob winning is 0.5. Whoever wins three games in total wins the jackpot. Alan wins two games and Bob wins one game of the first three; however, something happens and the game is interrupted. As they are unable to continue playing they need to divide up the jackpot based on the current results. How do you think the money should be divided given that Alan has won two games and Bob has only won one? (Answer in the video)
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Sample space and events:
The sample space of an experiment refers to the set of all possible outcomes.
The probability of an event is a measure of the chance that the event will occur. For an event, \(A\), the probability is given by \[Pr(A)=\frac{n(A)}{n( \varepsilon)}\] where \(n(A)\) represents the number of outcomes of \(A\) and \({n(\varepsilon)}\) represents the total number of outcomes in the sample space. There are two important rules for probability:
The sample space of an experiment refers to the set of all possible outcomes.
- Events are often labelled with capital letters (\(A\), \(B\), \(C\), \(D\), ...).
- Set notation can be used to represent the events in a sample space. For example, \(\varepsilon=\left \{ A,B,C,D,... \right \} \).
The probability of an event is a measure of the chance that the event will occur. For an event, \(A\), the probability is given by \[Pr(A)=\frac{n(A)}{n( \varepsilon)}\] where \(n(A)\) represents the number of outcomes of \(A\) and \({n(\varepsilon)}\) represents the total number of outcomes in the sample space. There are two important rules for probability:
- All probabilities are between 0 and 1 inclusive: \(0 \leq Pr(A) \leq 1\)
- The sum of all probabilities must equal 1: \(Pr(A)+Pr(B)+Pr(C)+...=1\)
8A - Content video: Summary of notation
This video covers the theory and several examples relating to the notation used in probability.
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More notes here :)
8A - Example 1: Determining probabilities for equally likely outcomes
Suppose that one card is randomly drawn from a shuffled deck of 52 cards. Determine the probability of each of the following events occurring:
(a) A heart is drawn. (b) A Jack is drawn. (c) A red Jack is drawn. (d) A red Jack is not drawn. |
8A - Example 1: Video solution
8A - Example 1: Practice
Question 1: ABC Question 2: ABC 8A - Example 1: Solutions
Question 1: ABC Question 2: ABC |
8A - Example 2: Determining probabilities for equally likely outcomes
A random experiment consist of four outcomes: \(\varepsilon =\left \{ A,B,C,D \right \}\). The probability of event \(A\) occurring is equal to the probability of event \(B\) occurring. The probability of event \(C\) occurring is half the probability of event \(A\) occurring. Finally, the probability of event \(D\) occurring is four times the probability of event \(C\) occurring. Find the probability of each of the events in the sample space.
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8A - Example 2: Video solution
8A - Example 2: Practice
Question 1: ABC Question 2: ABC 8A - Example 2: Solutions
Question 1: ABC Question 2: ABC |