Question

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?

Answer 1

The probability that the next two balls are blue is
`(5)/(32)`

Explanation:

There is a total number of 12 balls in the jar (7 Red and 5 blue), if the first marble drawn is a given, that is it is a Red marble, then following the instruction the Red marble and two more Red marbles are added. Therefore making the total number of marbles in the jar to be 14 marbles (9 red and 5 blue).

FIRST EVENT: So the probability of drawing the second marble to be a blue marble becomes = 5/14 [this is the number of blue marbles/ total number of marbles in the jar].

Thereafter the blue marble is returned and two more blue marbles are added to the jar making a total of 16 marbles (9 red and 7 blue}.

SECOND EVENT: So the probability of drawing the third marble to be a blue marble becomes = 7/16 [this is the number of blue marbles/ total number of marbles in the jar].

However, this is not the final answer because the first event and the second event must occur together, therefore, one has to multiply the first events probability and the second events probability to get the probability we are looking for.

So, the probability of picking the next two to be blue = 5/14*7/16 (seven can reduce the 14 to a 2 based on division)

Therefore the probability = 5/32 (the 2 multiplies the 16)