a) 0.0260
b) 0.0681
Explanation:
a)
The bag contains:
r = 9 (number of red marbles)
w = 5 (number of white marbles)
b = 6 (number of blue marbles)
So, the total number of marbles in the bag at the beginning is:
At the 1st attempt, the probability of choosing a red marble is:
(1)
At the 2nd attempt, the 1st red marble is not placed back, so now the number of marbles is (n-1), while the number of red marbles left is (r-1). So the probability of choosing another red marble at the 2nd attempt is
(2)
With a similar argument, the probabilities of selecting a red marble in the 3rd and 4th attempt are
(3)
(4)
Therefore, the probability of drawing 4 red marbles in the first 4 attempts without replacing is:
b)
At the 1st draw, the probability that the marble is not red is:
At the 2nd draw, there are 9 red marbles left and 19 total marble left. So, the probability of NOT drawing a red marble is:
At the 3rd draw, there are 9 red marbles left and 18 total marbles left. So, the probability of NOT drawing a red marble is:
Finally, with a similar argument the probability of NOT drawing a red marble at the 4th and last attempt is:
So, the total probability of drawing 4 non-red marbles in the first 4 attempts is: