Question

A bag 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.

Answer 1

the correct answer is 4/25 i just did this question

Answer 2

Answer: 4/25

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Step-by-step 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.