A bag contains 9 red marbles, 7 white marbles, and 7 blue marbles. You draw 4 marbles out at random, without replacement. What is the probability that all the marbles are red?

Answer 1

There are 23 total marbles and 9 red marbles.

The probability the first marble is red is 9/23, leaving 22 total marbles and 8 red ones.

The probability the second marble is red is 8/22, leaving 21 total marbles and 7 red ones.

The probability the third marble is red is 7/21, leaving 20 total marbles and 6 red ones.

The probability the fourth marble is red is 6/20.

The probability all four marbles are red is 9/23 * 8/22 * 7/21 * 6/20.

Answer 2

There are 23 total marbles (9 red, 7 white, and 7 blue). You want to select 4 marbles randomly without replacement. We want to know the probability of selecting 4 red marbles.

In this case, we have 3 different colors. By the formula (1 + 1 + 1)ⁿ = 3ⁿ, we can see how many possible outcomes of selecting 4 marbles randomly. Let n = 4.

There are 81 possible outcomes. We want to see which one has 4 red marbles. Only 1 possible outcome will give us that.

Therefore, P(4 red marbles) = 1/81 ≈ 0.01235.