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

Question

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

Explanation / Answer

Solution:

Given,there are

5 red marbles, 7 blue marbles.

given that the first marble drawn is red ,therefore , it is replaced alng with another red marblr

now the marbles in the jar are,

6 red marbles , 7 blue marbles.

the probability of drawing a blue ball = 7 / 13

now say the the second ball drawn is blue and the blue ball is replaced along with another blue ball.

now the marbles in the jar are

6 red marbles , 8 blue marbles.

the probability of drawing a blue ball in the third draw = 8 / 14

combined probability,

the probability the last two balls are blue given the first ball is red = ( 7 / 13 ) * ( 8 / 14 )

= 0.30769

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