If you have 30 white lego bricks, 42 red lego bricks, and 45 black lego bricks and you pull them out of a bag one at a time until one is left, what is the probability the last brick will be black

It would be the same as the probabity of pulling our a black first.

Pr=45/totalbricks

To find the probability that the last brick will be black, we need to calculate the ratio of the number of black bricks to the total number of bricks. Here's how you can do it step by step:

Step 1: Determine the total number of bricks.
The total number of bricks is the sum of the white, red, and black bricks:
Total bricks = white bricks + red bricks + black bricks

Total bricks = 30 + 42 + 45 = 117

Therefore, there are a total of 117 bricks.

Step 2: Calculate the probability of selecting a black brick on the first draw.
The probability of selecting a black brick on the first draw is the number of black bricks divided by the total number of bricks:
Probability of black on the first draw = number of black bricks / total bricks

Probability of black on the first draw = 45 / 117

Step 3: Calculate the probability of selecting a black brick after one is drawn.
After the first brick is drawn, the total number of bricks is reduced by one, but the number of black bricks remains the same. So, the probability of selecting a black brick on the second draw and subsequent draws will still be the number of black bricks divided by the total number of bricks:

Probability of black on the second draw = number of black bricks / (total bricks - 1)
Probability of black on the third draw = number of black bricks / (total bricks - 2)

So on, until only one brick is left.

Step 4: Multiply the probabilities together.
Since each draw is independent of the others, we can multiply the probabilities of selecting a black brick at each successive draw to find the probability that the last brick will be black.

Probability of last brick being black = Probability of black on the first draw × Probability of black on the second draw × ... × Probability of black on the nth-1 draw × Probability of black on the nth draw

In this case, since there are 117 bricks, we need to multiply the probabilities of selecting a black brick 116 times.

Therefore, the final probability would be:

Probability of last brick being black = (45 / 117) × (45 / 116) × (45 / 115) × ... × (45 / 1)

Calculating this large product would give you the probability of the last brick being black.