Question

A bag contains 10 red marbles, 10 white marbles, and 7 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red?

What is the probability that exactly two of the marbles are red?

What is the probability that none of the marbles are red?

Answer 1

The probability of drawing all red marbles is approximately 0.0276, the probability of drawing exactly 2 red marbles is approximately 0.4667, and the probability of drawing no red marbles is approximately 0.1027.

Step-by-step explanation:

To find the probability of drawing 5 red marbles out of 27 marbles without replacement, we need to calculate the probability of each draw being red.

First, let's find the probability that all 5 marbles are red:

P(1st draw is red) = 10/27

P(2nd draw is red) = 9/26 (There are now 26 marbles left, and 9 are red)

P(3rd draw is red) = 8/25

P(4th draw is red) = 7/24

P(5th draw is red) = 6/23

Now, we can calculate the probability by multiplying the probabilities of each draw:

P(all marbles are red) = (10/27) * (9/26) * (8/25) * (7/24) * (6/23)

≈ 0.0276

Similarly, to find the probability that exactly 2 marbles are red:

P(exactly 2 red marbles) = C(10, 2) * C(17, 3) / C(27, 5)

≈ 0.4667

And to find the probability that none of the marbles are red:

P(no red marbles) = C(17, 5) / C(27, 5)

≈ 0.1027