Lesson: Challenging Problem Solving - 27t04

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:

_____
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:
_____

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