A bag contains 8 red marbles 5 white marbles and 10 blue mar

A bag contains 8 red marbles, 5 white marbles, and 10 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red?

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 :

Solution

There are 23 marbles here.

Hence, there are 23C5 = 33649 ways to get 5 marbles.

a)

There are 8C2 = 28 ways to get 2 red marbles.

There are 15C3 = 455 ways to get not red marbles.

That makes 28*455 = 12740 ways.

Hence,

P = 12740 / 33649 = 0.37861452 [ANSWER]

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B)

There are 15C5 = 3003 ways to get 5 not red marbles.

Thus,

P(no red) = 3003/33649 = 0.089244851 [ANSWER]