I am having a tough time trying to understand the concept of probability and figuring out which is the right way to solve this problem. So I would really appreciate a lot if you can help me with this question
Problem: There are 5 red balls and 5 yellow balls. If we make 3 draws from this set, without replacing the ball drawn in each set, what is the probability that in the end we have drawn at least one red ball.
Method 1:
Calculate the probability of not drawing any red ball in all three draws and subtract that from 1.
The probability of drawing 3 yellow balls in succession : 5/10 * 4/9 * 3/8
So then the probability of drawing at least one red ball is 1-(5/10 * 4/9 * 3/8) = 11/12
Method 2:
Create the possible color combinations that the 3 draws can produce. I can come up with only 8 such combinations:
RRR, YYY, YRR, YRY, YYR, RRY, RYR, RYY
So based on these combinations I see that there is only 1 combination that has no red ball. So isthe probability of drawing a red ball then 7/8?
Which is the right answer and the right way of solving this problem.
Best Answer
The first is correct. In your second method you haven’t taken into account the fact that the eight different outcomes have different probabilities.