A bag contains 5 red marbles, 6 white marbles, and 8 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red?

Question

The probability that all the marbles are red is?
What is the probability that exactly two of the marbles are red?
The probability that exactly two of the marbles are red is ?
What is the probability that none of the marbles are red?
The probability of picking no red marbles is ?

Answer 1

prob(all 5 are red)
= (5/19)(4/18)(3/17)(2/16)(1/15)
= 1/11628

or , if you know how to calculate combinations
= C(5,5)/C(19,5)
= 1/11628

from here we can do
prob(no red) = 1 - 1/11628 = 11627/11628

prob(exactly 2 are red)
= C(5,2)xC(14,3)/C(19,5)
= 10(364)/11628
= 91/2907

Answer 2

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