Marble Probability Problem

Question

A bag contains 300 marbles. Some are red, and the rest are blue. The ratio of red marbles to blue marbles is 7:5. Suppose that 4 marbles are drawn from the bag at random and without replacement. What is the probability that all four marbles drawn are red?

Please explain your work. We were given the correct answer but still aren't sure how to solve the problem.

Answer 1

If there are 300 marbles, and the ratio of ^red/_blue is ⁷/₅ then there are 175 red marbles and 125 blue marbles.

The probability that the first marble drawn is red is ¹⁷⁵/₃₀₀

The probability that the second marble drawn is red if the first marble drawn is red is ¹⁷⁴/₂₉₉

The probability that the third marble drawn is red if the first two are also red is ¹⁷³/₂₉₈

And the probability that the fourth marble drawn is red if the first three are red is ¹⁷²/₂₉₇

The probability of all four happening is

¹⁷⁵/₃₀₀ * ¹⁷⁴/₂₉₉ * ¹⁷³/₂₉₈ * ¹⁷²/₂₉₇