A bag contains 8 white, 6 black and 4 red discs. They are selected at random and not replaced. What is the probability that there is at least one black disc in the first four discs drawn out of the bag?
prob that the first 4 drawn contain NO black
= (12/18)(11/17)(10/16)(9/15) = 11/68
so prob of at least 1 black
= 1 - 11/68
= 57/68
To find the probability of getting at least one black disc in the first four draws, we need to calculate the probability of drawing no black discs in the first four draws and then subtract it from 1.
Let's break it down step by step:
Step 1: Calculate the total number of ways we can choose 4 discs out of the available 18 discs (8 white, 6 black, and 4 red). This can be calculated using the combination formula, also known as "nCr":
Total ways = 18C4 = (18!)/(4!(18 - 4)!) = 3060
Step 2: Calculate the number of ways we can choose 4 discs without any black discs. Since we don't want any black discs, we can only choose from the 8 white and 4 red discs:
Ways without black = 12C4 = (12!)/(4!(12 - 4)!) = 495
Step 3: Calculate the probability of not getting any black discs in the first four draws:
Probability without black = Ways without black / Total ways = 495 / 3060 ≈ 0.1618
Step 4: Calculate the probability of getting at least one black disc:
Probability with at least one black = 1 - probability without black = 1 - 0.1618 = 0.8382 or approximately 83.82%
Therefore, the probability of having at least one black disc in the first four draws is approximately 0.8382 or 83.82%.