Final answer:
The probability of drawing both red balls is 1/35. The probability of drawing one red and one black ball is 1/7. The probability of drawing one white ball is 8/15.
Step-by-step explanation:
(i) Probability that both balls are red:
The probability of drawing the first red ball is 3/15, as there are 3 red balls out of a total of 15 balls. After drawing the first red ball, there are 2 red balls left out of 14 balls in total for the second draw. Therefore, the probability of drawing the second red ball is 2/14.
To find the probability of both balls being red, we multiply the probabilities of each draw: 3/15 * 2/14 = 1/35.
(ii) Probability that one ball is red and the other is black:
The probability of drawing a red ball at the first draw is 3/15. After drawing a red ball, the probability of drawing a black ball on the second draw is 5/14, as there are 5 black balls left out of 14 balls in total. Since the order of drawing does not matter, we multiply this probability by 2 to account for the possibility of drawing a red ball first and then a black ball, or vice versa: 3/15 * 5/14 * 2 = 1/7.
(iii) Probability that one ball is white:
The probability of drawing a white ball on the first draw is 7/15. The probability of drawing a non-white ball on the first draw is 1 - (7/15) = 8/15. Since we are only interested in the probability of drawing one white ball, we multiply this probability by 2 to account for the possibility of drawing a non-white ball first and then a white ball, or vice versa: 8/15 * 7/14 * 2 = 8/15.