Three balls are drawn one at a time without replacement from an urn that contains four white and six red balls what is the probability of drawing a red ball on the third draw?

P(R on the third draw) = 3/5 = 0.60 = 60%

To calculate the probability of this event you have to consider all the possible outcomes that give a Red ball on the third draw. They are four:

[1R,2R,3R], [1R,2W,3R], [1W,2R,3R], [1W,2W,3R].

The probability for these four events are:

1.- P(1R,2R,3R) = (6/10)(5/9)(4/8) = 1/6

2.- P(1R,2W,3R) = (6/10)(4/9)(5/8) = 1/6

3.- P(1W,2R,3R) = (4/10)(6/9)(5/8) = 1/6

4.- P(1W,2W,3R) = (4/10)(3/9)(6/8) = 1/10

Then the probability looked for is the sum of all four:

P(R on the third draw) = 1/6 + 1/6 + 1/6 + 1/10 = 3/5 = 0.60 = 60%