A bag contains 5 red marbles, 9 white marbles, and 5 blue marbles. You draw 4 marbles out at random, without replacement. What is the probability that all the marbles are red?

For first red marble, 5/19. For second red marble, (5-1)/(19-1), continue on for 3rd and 4th marbles and then multiply.

To find the probability that all the marbles drawn are red, we need to calculate the ratio between the number of favorable outcomes (drawing all red marbles) and the number of possible outcomes when drawing 4 marbles out of the bag.

The total number of marbles in the bag is 5 + 9 + 5 = 19.

The number of ways to choose 4 marbles out of 5 red marbles is given by the combination formula: C(5, 4) = 5! / (4! * (5-4)!) = 5.

The total number of ways to choose 4 marbles out of 19 marbles is given by C(19, 4) = 19! / (4! * (19-4)!) = 3,876.

Therefore, the probability of drawing all red marbles can be calculated as follows:

P(all red) = Number of ways to draw all red marbles / Total number of ways to draw 4 marbles = 5 / 3,876 ≈ 0.00129.

So, the probability that all marbles drawn are red is approximately 0.00129 or 0.129%.

To find the probability that all 4 marbles drawn are red, we need to calculate the ratio of favorable outcomes to total outcomes.

First, let's determine the total number of marbles in the bag. We have 5 red marbles, 9 white marbles, and 5 blue marbles, so the total number of marbles is 5 + 9 + 5 = 19.

Next, we need to calculate the number of ways to choose 4 red marbles out of the 5 available. This can be done using combinations. The formula to calculate combinations is:

C(n, k) = n! / (k!(n - k)!)

In this case, n represents the number of red marbles (5) and k represents the number of marbles we wish to draw (4). So the number of combinations to choose 4 red marbles out of 5 is:

C(5, 4) = 5! / (4!(5 - 4)!) = 5! / (4!1!) = 5

Finally, we calculate the probability by dividing the number of favorable outcomes (choosing 4 red marbles) by the total number of outcomes (drawing any 4 marbles):

P(4 red marbles) = C(5, 4) / C(19, 4) = 5 / C(19, 4)

Now, the number of ways to choose any 4 marbles out of 19 can be calculated using combinations as well:

C(19, 4) = 19! / (4!(19 - 4)!) = 19! / (4!15!) = (19 * 18 * 17 * 16) / (4 * 3 * 2 * 1) = 4,845

Therefore, the probability that all 4 marbles drawn are red is:

P(4 red marbles) = 5 / 4,845 ≈ 0.001031209

So, the probability is approximately 0.001 or 0.1%.