In: Statistics and Probability
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?
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