There are 36 pieces of building blocks in a bag: 9 each of blue, green, red, and yellow. Four pieces are chosen at random. Identify the probability that all four of the pieces are red.
4/8415
12/935
8/19,635
2/935
9/36 * 8/35 * 7/34 * 6/33 = 2/935
To find the probability that all four of the pieces chosen are red, we need to calculate the ratio of the number of favorable outcomes (in this case, all four red pieces) to the total number of possible outcomes.
First, let's determine the total number of possible outcomes. We start with 36 building blocks in the bag. For the first piece chosen, there are 36 possibilities. For the second piece, there are 35 left, for the third piece there are 34, and for the fourth piece, there are 33 remaining. Therefore, the total number of possible outcomes is 36 * 35 * 34 * 33.
Next, let's determine the number of favorable outcomes, which is the number of ways to choose all four red pieces out of the nine red ones. Using the combination formula, we can calculate it as C(9, 4) which is equal to 9! / (4! * (9 - 4)!).
Calculating this, we get C(9, 4) = 9! / (4! * 5!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 126.
Therefore, the probability of choosing all four red pieces is 126 / (36 * 35 * 34 * 33). Evaluating this expression, we find the probability to be 2/935.
So, the correct answer is 2/935.