Question

an urn contains one red ball and one blue ball. a box of extra red and blue balls lie nearby. george performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to the urn. after the four iterations the urn contains six balls. what is the probability that the urn contains three balls of each color?

Answer 1

The probability that the balls are the same color is x + 10/60

Where x is the number of blue balls there are in the second urn.

Given,

The quantity of blue balls in the second urn will be called x. The number of red balls would be 20 - x given that there are 20 balls in this urn.

In order to find the probability that the balls are the same colour, we must assume that they are both either blue OR red. (Since we're using "or," we can infer that we'll add the probabilities of both outcomes.

1) P(both balls are blue) = P(both balls are the same colour) + P ( both balls are red).

2) Next, we'll determine the probability that both balls are blue (this will require multiplication because we need both ball 1 and ball 2 to be blue):

P(ball 1 is blue) x P = P(both balls are blue) (ball 2 is blue)

P(both blue balls) = = (1/6)* (x/20) = x/120

3) The procedure is the same as when both balls are blue to get the probability that both balls are red.

P(ball 1 is red) x P = P(both balls are red) (ball 2 is red)

When both balls are red, P(both are red) = = (1/6) * (20-x)/20 = 20- x/12

4) Returning to point 1 and substituting:

P(the same color of both balls) = x/120 + (20 - x)/120

= 2x + 20/120

= x + 10/60

That is,

The probability of the balls having the same color are x + 10/60.

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