A bag contains 6 red marbles, 2 blue marbles and 7 green marbles. If two marbles are drawn out of the bag, what is the probability to the nearest 1000th, that both marbles drawn will be red ?
To find the probability that both marbles drawn will be red, we need to first calculate the total number of ways to draw 2 marbles out of the bag and then calculate the number of ways to draw 2 red marbles.
Total number of marbles = 6 (red) + 2 (blue) + 7 (green) = 15
Total number of ways to draw 2 marbles out of the bag = 15C2 = 15! / ((15-2)! * 2!) = 15! / (13! * 2!) = 105
Number of ways to draw 2 red marbles = 6C2 = 6! / ((6-2)! * 2!) = 6! / 4! * 2! = 15
Therefore, the probability of drawing 2 red marbles = Number of ways to draw 2 red marbles / Total number of ways to draw 2 marbles = 15 / 105 = 3 / 21 = 1 / 7 = 0.143
So, the probability, to the nearest 1000th, that both marbles drawn will be red is 0.143.