Suppose a bag of marbles has 4 green, 2 red, 5 yellow, 1 brown, and 7 blue marbles. What is the probability of picking a green marble, replacing it, and then picking a brown marble?
prob(green, then brown)
= (4/19)(1/19) = 4/361
To find the probability of picking a green marble, replacing it, and then picking a brown marble, we can use the concept of probabilities and multiplication.
Step 1: Calculate the probability of picking a green marble:
In this case, there are 4 green marbles out of a total of 19 marbles (4 + 2 + 5 + 1 + 7). So, the probability of picking a green marble is 4/19.
Step 2: Calculate the probability of picking a brown marble:
Now that we have replaced the green marble back into the bag, the total number of marbles remains the same. There is 1 brown marble out of 19 marbles. Therefore, the probability of picking a brown marble is 1/19.
Step 3: Multiply the probabilities:
To find the probability of both events happening, we multiply the individual probabilities together. So, the probability of picking a green marble and then a brown marble is (4/19) * (1/19).
Using these calculations, the probability of picking a green marble, replacing it, and then picking a brown marble is approximately 0.0112 or 1.12%.