What is the probability of drawing a red checker from a bag of 9 black checkers and 6 red checkers, replacing it, and drawing it again?
To determine the probability of drawing a red checker from a bag of black and red checkers, with replacement, you need to know the total number of checkers and the number of red checkers.
In this case, there are 9 black checkers and 6 red checkers in the bag, for a total of 15 checkers.
Since you are replacing the checker after each draw, the total number of checkers remains the same for subsequent draws. Therefore, the probability of drawing a red checker on the first draw is 6/15, or 2/5.
Similarly, the probability of drawing a red checker on the second draw (assuming the first draw was a red checker) is also 6/15, or 2/5.
To find the probability of independent events occurring in succession, you multiply the individual probabilities. So, the probability of drawing a red checker on the first draw and a red checker on the second draw is (2/5) * (2/5), which simplifies to 4/25.
Therefore, the probability of drawing a red checker from a bag of 9 black checkers and 6 red checkers, replacing it, and drawing it again is 4/25.