Lauretta J. Fox
Two events are dependent if the occurrence of one of the events affects the probability of the occurrence of the other. Consider a box that contains seven white, five green, and four blue pieces of chalk. If two pieces of chalk are drawn from the box, and the first piece is not replaced before the second piece is drawn, the outcome of the first selection affects the outcome of the second drawing. The probability of drawing a piece of blue chalk the first time is 4/16 or 1/4. If a piece of blue chalk is drawn first, then three of the remaining pieces of chalk are blue, and the probability of getting a piece of blue chalk on the second draw is 3/15 or 1/5.
The probability that two dependent events will happen may be expressed as follows: If pl is the probability that event X will happen and, after X has happened, p2 is the probability that event Y will happen, then the probability that the events will occur in the order X,Y is p1p2, the product of their respective probabilities.
Exercises:
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1.) A bag contains five green marbles, four yellow marbles, and nine white marbles. If two marbles are drawn in succession, and the first marble is not replaced before the second is drawn, what is the probability that:
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a.) the second marble is yellow, if the first marble drawn is green?
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b.) the second marble is white, if the first marble drawn is yellow?
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c.) both marbles are green?
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d.) both marbles are yellow?
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e.) both marbles are white?
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2.) A boX contains ten slips of paper. Three slips are marked with the letter G, two slips are marked M, and five slips are marked K. If two slips of paper are drawn in succession, and the first is not replaced before the second is drawn, what is the probability that:
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a.) the first slip is marked G, and the second is marked K?
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b.) the first slip is marked G, and the second is marked H?
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c.) the first is marked H, and the second is marked G?
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d.) the first is marked K, and the second is marked G?
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e.) the first is marked H, and the second is marked K?
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f.) the first slip is marked K, and the second slip is marked M?
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g.) both slips are marked G?
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h.) both slips are marked M?
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i.) both slips are marked K?
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3.) The probability that Mr. Smith will be elected president is 5/7, and if he is elected, the probability that he will appoint Mr. Jones attorney general is 2/3. Find the probability that Mr. Jones will be attorney general.
