A bag has 5 red marbles, 6 blue marbles and 4 black marbles. What is the probability of picking a
blue marble, replacing it, and then picking a black marble?
what is (6/15)(4/15) ?
To find the probability of picking a blue marble, replacing it, and then picking a black marble, we need to first calculate the individual probabilities of picking a blue marble and a black marble.
The probability of picking a blue marble can be calculated by dividing the number of blue marbles by the total number of marbles in the bag. In this case, there are 6 blue marbles and a total of 5 red marbles + 6 blue marbles + 4 black marbles = 15 marbles.
So, the probability of picking a blue marble is 6/15, which simplifies to 2/5.
Since the marble is replaced before the second pick, the number of blue marbles and black marbles remains the same. Therefore, the probability of picking a black marble is also 6/15 or 2/5.
To find the probability of both events happening, we need to multiply the probabilities of picking a blue marble and picking a black marble. Since the two events are independent (the outcome of the first pick does not affect the outcome of the second pick), we can simply multiply the individual probabilities.
So, the probability of picking a blue marble, replacing it, and then picking a black marble is (2/5) * (2/5) = 4/25.