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? write your answer as a fraction.

Explanation:

Step1: Calculate probability of first - red marble

The total number of marbles is $2 + 3=5$. The number of red marbles is 2. So the probability of picking a red marble on the first draw, $P_1$, is $\frac{2}{5}$.

Step2: Calculate probability of second - red marble

Since the marble is replaced, the total number of marbles is still 5 and the number of red marbles is still 2. So the probability of picking a red marble on the second draw, $P_2$, is $\frac{2}{5}$.

Step3: Calculate probability of both events

For independent events, the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=\frac{2}{5}\times\frac{2}{5}=\frac{4}{25}$.

Answer:

$\frac{4}{25}$