# Determining probabilities using tree diagrams and tables

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##### Intros
###### Lessons
1. Introduction to Probability
• What is probability?
• How to write probability as a fraction, decimal, and percent?
• How to draw a tree diagram?
2. How to draw a tree diagram?
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##### Examples
###### Lessons
1. Ken flips a coin and draws out a marble from a bag with 5 marbles of different colours: green, blue, red, orange and yellow.
1. Draw a tree diagram to show the sample space.
2. What is the probability of P(H, R)?
3. What is the probability of not getting the head?
2. Two standard six-sided dice are rolled.
1. Draw a table to display the sample space.
2. What is the probability of P(doubles)?
3. What is the probability of P(sum less than 10)?
4. What is the probability of P(two even numbers)?
3. Assume that there will only be rain or sunshine in the next 4 days. Draw a table to display the sample space. Determine the probability of:
1. There is rain 4 days in a row.
2. There is rain or no rain 4 days in a row.
3. There is rain in any 2 days.
4. There is rain in at least 1 day.
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##### Practice
###### Topic Notes
Tables and tree diagrams are useful tools to calculate probabilities. With them, you can list all the possible outcomes of an event (sample space) in a clear and easy to understand way. Therefore, we can determine the probabilities of events effectively.