0002359, therefore all we must now do is multiply the probability above by the number of arrangements. ALL of these arrangements will have the same probability of occurring = 0. For instance you could get RRBBRRBBRRRB or BBBBBRRRRRRR or any other arrangement. Therefore the probability of the second being red given the first is red = 40/59 The third red = 39/58 The 4th red = 38/57 The 5th red = 37/56 the 6th red = 36 /55 the 7th red = 35 /54 The 8th blue = 19/53 (there are 19 blue in the bag) The 9th blue = 18/52 The 10th blue = 17/51 The 11th blue = 16/50 The 12th blue = 15/49 Therefore the probability of RRRRRRRBBBBB = all these individual probabilities multiplied together = (41 * 40 * 39 * 38 * 37 * 36 * 35 * 19 * 18 * 17 * 16 * 15) / (60 * 59 * 58 * 57 * 56 * 55 * 54 * 53 * 52 * 51 * 50 * 49) (If I have input it into my calculator correctly this equals 0.0002359 to seven decimal places) NOW you have to realise that there are more than one way to get 7 red and 5 blue. Lets first work out the probability of RRRRRRRBBBBB The First being a red = 41/60 There now remain 59 marbles in the bag and 40 are red. Firstly working out the probability of a typical string of 7 red and 5 blue and then secondly the number of ARRANGEMENTS there are of 7 red and 5 blue. I am going to assume the marbles are not replaced. There are 60 total marbles -There are 41 red marbles.
If 12 marbles from 60 are chosen at random what is the probability of selecting exactly 7 red marbles.