Abag contains 2 red marbles and 3 black marbles. if abby picks a marble without looking, returns it to the bag, and then draws a second marble, what is the probability that both marbles are red? give the answer as a fraction in simplest form.

4/25



Explanation:

Let's define two events A and B
A = event of selecting red on the first draw
B = event of selecting red on the second draw

P(A) is the notation that means "probability of event A occurring"

P(A) = 2/5 because there are 2 red marbles out of 5 total (2 red + 3 black = 5)
Similarly, P(B) = 2/5 as well because A and B deal with the same color red, and because Abby put the first marble back

Multiply the probabilities
P(A and B) = P(A)*P(B) ... see note below
P(A and B) = (2/5)*(2/5)
P(A and B) = (2*2)/(5*5)
P(A and B) = 4/25 which is the answer

Note: the equation used is only valid if events A and B are independent, which they are in this case. The fact we put the marble back means the chances of picking red are the same as before.

Bis the answer! hope this

The second and fourth answer are correct