A bag has 5 red marbles, 6 blue marbles and 4 black marbles. What is the probability of picking a
black marble, replacing it, and then picking a black marble?
To calculate the probability of picking a black marble, replacing it, and then picking another black marble, we need to consider the individual probabilities.
Step 1: Picking a black marble
The probability of picking a black marble from the bag is given by the ratio of the number of black marbles to the total number of marbles:
P(black marble) = number of black marbles / total number of marbles
P(black marble) = 4 / (5 + 6 + 4) = 4 / 15
Step 2: Replacing the first black marble
Since we're replacing the first black marble back into the bag, the number of black marbles remains the same at 4, and the total number of marbles also remains the same at 15.
Step 3: Picking a black marble again
The probability of picking a black marble again is the same as the probability in Step 1, as the number of black marbles and total number of marbles have not changed:
P(black marble) = 4 / 15
To find the probability of both events happening (picking a black marble and then picking another black marble), we multiply the probabilities from the individual steps:
P(both events happening) = P(black marble) * P(black marble) = (4/15) * (4/15) = 16/225.
So, the probability of picking a black marble, replacing it, and then picking another black marble is 16/225.
To find the probability of picking a black marble, replacing it, and then picking another black marble, we can multiply the individual probabilities of each event.
First, let's calculate the probability of picking a black marble on the first draw.
The total number of marbles in the bag is 5 (red) + 6 (blue) + 4 (black) = 15.
The probability of picking a black marble on the first draw is the number of black marbles divided by the total number of marbles: 4/15.
Since we are replacing the marble after the first draw, the number of black marbles and the total number of marbles remain the same.
Therefore, the probability of picking a black marble on the second draw is also 4/15.
To find the probability of both events happening, we multiply the probabilities:
Probability = (4/15) × (4/15) = 16/225.
So, the probability of picking a black marble, replacing it, and then picking a black marble is 16/225.
total marbles: 15
so, P(black,black) = 4/15 * 4/15