Question

A bag contains 6 red and 8 white balls. One ball is drawn at random. What is the probability that the drawn is white?

Answer 1

The probability that the drawn is a white ball is 8/14.

Answer 2

If it's three or more, the probability is 100%.

However, I will assume that you intend to draw only two balls and that you don't replace the first ball in the bag for the second draw.

So you draw one ball. The probability that it's red is 8/14 = 4/7.

You draw again. The probability of getting a second red is 7 (red balls remains) / 13 (balls remaining).

Assuming that the results of the first and second draws are independent,the probability of drawing two red balls is therefore (4/7)*(7/13) = 4/13.

Now, suppose instead of a red on the first draw you got white. The probability of this is 6/14 = 3/7.

Given the first ball is white, the probability of drawing a second white is 5/13.

So the probability of drawing two whites is (3/7)*(5/13) = 15/91.

The outcomes of drawing two reds or two whites are independent of each other, so you can add the probabilities to get the probability of drawing two balls of the same colour, i.e.

4/13 + 15/91 = 43/91

If you prefer to express it as a percentage, it's approximately 47.25%.