Lesson: Challenging Problem Solving - 27t05

Dependent Probability

Basic probability, the topic of the previous screen, is also known as independent probability - the chance of selecting a marble was not dependent on any previous outcome. Only the relative numbers of marbles in the box at the moment of selection determined the probability of choosing a certain marble. Dependent probability, on the other hand, refers to situations in which the chance of an outcome occurring is influenced by a previous outcome. In such instances, the probability of both outcomes occurring is: Probability of Outcome 1 Probability of Outcome 2 = Probability of Outcomes 1 and 2 The following example will illustrate:

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What is the probability that a blue marble will be chosen on the first draw? Enter your response into the text box below and then click Continue.

Probability of blue on 1st draw: _____

What is the probability that a blue marble will be chosen on the second draw if a blue marble was chosen on the first draw? Enter your response into the text box below and then click Continue.

Probability of blue on 2nd draw: _____

Now compute the probability that BOTH the first and second marbles drawn will be blue.

Probability of choosing two blue marbles on 1st and 2nd draws: _____

Our first probability, , represents the chances of choosing a blue marble on the first draw; our second probability, , represents the chances of choosing a blue marble on the second draw. To find the combined probability of these two draws, we must multiply the two separate probabilities:

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Note that we did not reduce our first draw probability fraction until we obtained the combined probability of both draws. If we had reduced to , we would not have been able to calculate the correct probability for the second draw because the reduction would have changed our numerator and denominator:

Correct:

Incorrect:

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