Suppose you have a bag containing 2 black marbles and 3 red marbles. You reach into the bag, select a marble, see what color it is and replace it in the bag. Then you repeat this process a second time. What is the probability of picking a red marble both times?

Step-by-step explanation:

Given that the bag contains black and red marbles.

Number of black marbles in the bag = 2

Number of red marbles in the bag = 3

Total number of marbles in the bag = Number of black marbles + Number of red marbles = 2 + 3 = 5

Let us have a look at the formula for probability of an event E, which can be observed as:

Now, the marble chosen at first is replaced.

Therefore, the count remains the same.

Now, the required probability can be found as: