16.1 Determining probabilities using tree diagrams and tables

There’s going to be test in an hour but you didn’t review over the weekends. The test consists of multiple choice questions so you are going to try your luck and randomly choose an answer based on your gut feelings. There are a hundred questions with 4 choices each, what’s the probability of you passing the test if you were to pick just one letter for all your answers?

Probability is perhaps one the most interesting topics in math because you get to apply them in so many real life issues, like the probability of rain, the probability of accidents to occur and so on and so forth.

Probability is the measure of the chance of events to occur in a particular sample space. It can appear in percent or in fraction form. Probability is more like a simulation of events in a mathematical equation in order to predict possible outcomes. It can be computed using the formula

Outcome is defined as the result of the experiment. In your case, the outcome of answers for test question 1 can be A, B, C or D. Event is defined as the set of outcome of that certain experiment, like in your case, the event would be the answers to be letter A or B or C or D. Events can either be independent, and dependent.

Independent events are not affected by other events. There are four choices in each test question and in every item there can only be one answer, this answer is only for this item, it won’t affect the other questions. Your probability of getting the first item correct is ¼. Dependent events on the other hand are affected due to the past events, like the probability of drawing cards in a deck. Every time you draw a card, an outcome is pulled out from the possible pool of events that could occur.

In this chapter we will be learning how to determine probability using tree diagrams and tables. In the first part of the chapter we will get to solve probability problems using this technique while In the second part of this chapter, we will get to look into the solving for the probability of independent events.

After this chapter you can now be able to compute for the probability of events to occur and event the probability of you passing and failing the test. You can even calculate your probability of winning in a lottery

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Determining probabilities using tree diagrams and tables

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.


  • 1.
    Ken flips a coin and draws out a marble from a bag with 4 marbles of different colours: green, blue, red, orange and yellow.
  • 2.
    Two standard six-sided dice are rolled.
  • 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:
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Determining probabilities using tree diagrams and tables

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