Dana is going to draw marbles out of the bag. In the bag, there are 10 marbles. There are 4 black marbles, 5 white marbles, and 1 red marble. Dana choooses two marbles. After choosing the first one she put it back in the bag before choosing the second marble. What is the probability that both marbles she chooses are black? *
4 black out of 10 marbles, so
P(black) = 4/10
the two draws are independent, so multiply the probabilities.
To find the probability of both marbles being black, we need to calculate the probability of choosing a black marble on the first draw and then multiply it by the probability of choosing another black marble on the second draw.
First, let's find the probability of choosing a black marble on the first draw.
The total number of marbles in the bag is 10, and there are 4 black marbles. So the probability of choosing a black marble on the first draw is 4/10.
Since after choosing the first marble, Dana puts it back in the bag, the number of marbles and the number of black marbles remain the same for the second draw. Therefore, the probability of choosing another black marble on the second draw is also 4/10.
Now, we can find the probability of both marbles being black by multiplying the probabilities of the individual events:
Probability of first draw being black * Probability of second draw being black = (4/10) * (4/10) = 16/100 = 4/25
So, the probability that both marbles Dana chooses are black is 4/25.