Find the probability: picking a black checker from a bag of 9 black checkers and 6 red checkers, replacing it, and picking a red checker.
15 checkers in all, so
9/15 * 6/15 = ____
To find the probability, we need to determine the probability of each event and then multiply them together.
1. Picking a black checker from a bag of 9 black checkers and 6 red checkers:
- There are a total of 9 + 6 = 15 checkers in the bag.
- The probability of picking a black checker is 9/15, since there are 9 black checkers out of the total 15 checkers.
2. Replacing the black checker back into the bag:
- After the first pick, we are replacing the black checker back into the bag. This means the number of black checkers and the total number of checkers remain the same.
3. Picking a red checker:
- There are still 9 black checkers and 6 red checkers in the bag.
- The probability of picking a red checker is 6/15, since there are 6 red checkers out of the total 15 checkers.
Now, we can calculate the probability of both events happening:
P(picking a black checker and then picking a red checker) = P(picking a black checker) * P(picking a red checker)
= (9/15) * (6/15)
= 54/225
= 0.24 or 24%
Therefore, the probability of picking a black checker and then picking a red checker is 0.24 or 24%.
To find the probability of picking a black checker from the bag of 9 black checkers and 6 red checkers, replacing it, and then picking a red checker, you need to follow these steps:
Step 1: Find the probability of picking a black checker.
The bag contains a total of 9 black checkers and 6 red checkers. Since you are replacing the checker after each pick, the number of black checkers remains the same for the second pick. Therefore, the probability of picking a black checker on the first pick is:
Probability of picking a black checker = Number of black checkers / Total number of checkers
Probability of picking a black checker = 9 / (9 + 6) = 9/15 = 3/5
Step 2: Find the probability of picking a red checker.
After replacing the black checker, the bag still contains 9 black checkers and 6 red checkers. Since you are replacing the checker after each pick, the number of red checkers remains the same for the first pick. Therefore, the probability of picking a red checker on the second pick is:
Probability of picking a red checker = Number of red checkers / Total number of checkers
Probability of picking a red checker = 6 / (9 + 6) = 6/15 = 2/5
Step 3: Find the combined probability.
To find the combined probability of both events happening (picking a black checker and then picking a red checker), you need to multiply the probabilities from step 1 and step 2:
Combined probability = Probability of first event * Probability of second event
Combined probability = (3/5) * (2/5) = 6/25
Therefore, the probability of picking a black checker, replacing it, and then picking a red checker is 6/25.