A) To find the probability of drawing 3 blue marbles, we need to consider the total possible outcomes and the favorable outcomes.
Total possible outcomes: Choosing 6 marbles out of 24 (9 red + 10 white + 5 blue) is given by the combination formula: C(24, 6) = 134,596.
Favorable outcomes: Choosing 3 blue marbles out of 5 is given by the combination formula: C(5, 3) = 10.
Therefore, the probability of drawing 3 blue marbles is 10/134,596.
B) To find the probability of drawing the same number of each color, we need to consider the total possible outcomes and the favorable outcomes.
Total possible outcomes: Choosing 6 marbles out of 24 (9 red + 10 white + 5 blue) is given by the combination formula: C(24, 6) = 134,596.
Favorable outcomes: There are two ways to have the same number of each color:
1. Choosing 2 blue, 2 red, and 2 white marbles: C(5, 2) * C(9, 2) * C(10, 2) = 4,050.
2. Choosing 4 blue, 1 red, and 1 white marble: C(5, 4) * C(9, 1) * C(10, 1) = 450.
Therefore, the probability of having the same number of each color is (4,050 + 450) / 134,596.
C) To find the probability of none of the drawn marbles being red, we need to consider the total possible outcomes and the favorable outcomes.
Total possible outcomes: Choosing 6 marbles out of 24 (9 red + 10 white + 5 blue) is given by the combination formula: C(24, 6) = 134,596.
Favorable outcomes: Choosing 6 marbles without any red marbles: C(15, 6) = 5005.
Therefore, the probability of none of the drawn marbles being red is 5005 / 134,596.
D) To find the probability of all 6 marbles being the same color, we need to consider the total possible outcomes and the favorable outcomes.
Total possible outcomes: Choosing 6 marbles out of 24 (9 red + 10 white + 5 blue) is given by the combination formula: C(24, 6) = 134,596.
Favorable outcomes: There are three ways to choose all 6 marbles of the same color: C(9, 6) + C(10, 6) + C(5, 6) = 84.
Therefore, the probability of all 6 marbles being the same color is 84 / 134,596.
A bag contains 9 red marbles, 10 white, 5 blue. If six are drawn at random, what is the probability of
A) 3 blue
B) same number of each colour
C) none will be red
D) all 6 will be the same colour
1 answer