drawing a black checker from a bag of 9 black checkers and 6 red checkers, replacing it, and drawing a red checker
54/225
9/15 * 6/15 = ?
To solve this problem, we need to find the probability of drawing a black checker, replacing it, and then drawing a red checker from a bag containing 9 black checkers and 6 red checkers.
Step 1: Calculate the probability of drawing a black checker on the first draw.
Since there are 9 black checkers and a total of 9 black checkers + 6 red checkers = 15 total checkers in the bag, the probability of drawing a black checker on the first draw is 9/15 (as there are 9 favorable outcomes out of 15 possible outcomes).
Step 2: Calculate the probability of drawing a red checker on the second draw.
Since we are replacing the first checker, the total number of checkers in the bag remains the same (9 black checkers + 6 red checkers = 15 total checkers). The probability of drawing a red checker on the second draw is 6/15 (as there are 6 favorable outcomes out of 15 possible outcomes).
Step 3: Multiply the probabilities from Step 1 and Step 2 together.
To find the probability of both events happening, we multiply the probabilities from Step 1 and Step 2: (9/15) * (6/15) = 54/225, which simplifies to 6/25.
Therefore, the probability of drawing a black checker, replacing it, and then drawing a red checker is 6/25.