Suppose we draw 3 marbles from a jar containing 7 red and 5 blue marbles. At...

Suppose we draw 3 marbles from a jar containing 7 red and 5 blue marbles. At each stage, a ball is drawn and its color noted. Then the marble is returned to the jar along with another two marbles of the same color. Given that the ﬁrst marble is red, what is the probability that the next two are blue?

Solutions

Expert Solution

Given that first marble is Red; red marble is returned to jar and Two red marbles are added to the jar

Number of red marbles = 7+2 = 9

Number of blue marbles = 5

Total number of marbles = 14

Probability of drawing a blue marble in the next draw(second draw) = number of blue marbles / Total number of marbles = 5/14

Given that second draw is blue, blue marble is returned to jar two blue marbles are added to the jar

Number of red marbles in the jar = 9

Number of blue marbles = 5+2 =7

Total number of marbles = 9+7 = 16

Probability of drawing a blue marble in the next draw(third draw) = number of blue marbles / Total number of marbles = 7/16

Given that the ﬁrst marble is red, Probability that the next two are blue = Probability of drawing a blue marble in the second draw x Probability of drawing a blue marble in the third draw = (5/14)x(7/16) = 35/224= 0.15625

Given that the ﬁrst marble is red, Probability that the next two are blue = 0.15625

orchestra answered 1 year ago

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