If 3 marbles are drawn from a bag of 12 marbles consisting of three red, four white and five blue, without returning them to the bag, what is the probability that the first marble is red the second is white and the third is blue?

The probability of that happening is 1/22

Step-by-step explanation:

In order to find the probability, you need to start by finding the probability for each step. The probability of the first one being red is the number of red marbles divided by the total number of marbles.

3 red / 12 total.

3/12

1/4

Now the chance that the second is white is the total number of white marbles divided by how many are left in the bag.

4 white / 11 left

4/11

Lastly, the chance of the last one being blue is the number of blue marbles divided by the amount of total marbles left after two pulls.

5 blue/ 10 left

5/10

1/2

Now to find the overall probability of all 3 happening, we multiply all 3 probabilities together.

1/4 * 4/11 * 1/2 = 1/22

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)