drawing a red checker from bag of 9 black checksrs and 6 red checkers, replacing it and drawing another red checker
Billy takes two marbles, without replacement, from a bag that contains only six yellow marbles and three blue marbles.
What is the probability that he gets one marble of each color?
To draw a red checker from a bag of 9 black checkers and 6 red checkers, replacing it, and then draw another red checker, follow these steps:
1. Start with a bag containing 9 black checkers and 6 red checkers.
2. Reach into the bag and randomly draw one checker.
3. Note the color of the checker you drew. If it is red, go to step 4. If it is black, go to step 5.
4. Replace the checker you just drew back into the bag.
5. Reach into the bag again and randomly draw another checker.
6. Note the color of the second checker you drew. Whether it is red or black, you have completed the process.
You have now drawn a red checker from the bag, replaced it, and drawn another red checker.
To find the probability of drawing a red checker from a bag of 9 black checkers and 6 red checkers, replacing it, and then drawing another red checker, you'll need to follow these steps:
Step 1: Determine the probability of drawing a red checker on the first draw.
Since there are 6 red checkers out of a total of 9 black checkers + 6 red checkers, the probability of drawing a red checker on the first draw is 6/15 (or simplified, 2/5).
Step 2: Calculate the probability of drawing a red checker on the second draw, given that the first draw was a red checker.
Since we are replacing the first red checker back into the bag, the probability of drawing another red checker on the second draw remains the same, which is 2/5.
Step 3: Multiply the probabilities from both steps.
To calculate the probability of both events occurring, you multiply the probabilities together:
(2/5) * (2/5) = 4/25
Therefore, the probability of drawing a red checker, replacing it, and drawing another red checker is 4/25.
The probability of drawing a red checker = # of red checkers/total. Since the red checker is replaced, the probability of drawing red the second time is the same.
The probability of both/all events occurring is found by multiplying the probabilities of the individual events.
I hope this helps.