Lesson: Challenging Problem Solving - 27t09

Dependent Probability

[Page 27 of 37]

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:

A box contains 3 blue marbles, 2 green marbles, and 4 red marbles. If one marble is selected at random, and a second marble is selected without replacing the first, what is the probability that both marbles chosen are blue?

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:


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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 2^nd draw:


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

Probability of choosing two blue marbles on 1^st and 2^nd draws:
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Now use our sample question to determine the probability for each of the two scenarios that follow. For each one, enter your response into the textbox and then click Continue.

What is the probability that both marbles chosen are green?
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What is the probability that the first marble chosen is red, and that the second marble chosen is green?
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There are 4 red marbles out of a total of 9, so the probability of choosing green on the first draw is:.

If one red marble has been taken out and not replaced, we now have 8 marbles from which to choose. However, no green marble has been removed, so we have our original number of green marbles from which to select. Therefore, the probability of choosing green on the second draw is:.