Suppose you have 5 marbles in a bag: 3 red and 2 black. If you reach into the bag without looking and randomly pick out two marbles, what is the probability that both marbles are red?

(3/5)(2/4) = ?

To find the probability that both marbles drawn are red, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of marbles in the bag = 5 (3 red + 2 black)
Number of ways to choose 2 marbles out of 5 = 5C2 = (5!)/(2!(5-2)!) = 10

Number of favorable outcomes (both marbles are red) = 3C2 = (3!)/(2!(3-2)!) = 3

Therefore, the probability of drawing two red marbles is 3/10.

To determine the probability of picking out two red marbles from the bag, we need to calculate the ratio between the number of favorable outcomes (picking two red marbles) and the total number of possible outcomes (picking any two marbles).

First, let's calculate the total number of possible outcomes. When we randomly pick two marbles from the bag without looking, there are different combinations that can occur. We can use the formula for combinations, which is:

nCr = (n! / ((n - r)! * r!))

Here, 'n' represents the total number of marbles in the bag, and 'r' represents the number of marbles we want to pick. In this case, n = 5 and r = 2. So, plugging in the values:

5C2 = (5! / ((5 - 2)! * 2!))
= (5! / (3! * 2!))
= (5 * 4 * 3! / (3! * 2 * 1))
= (5 * 4) / (2 * 1)
= 10

Therefore, there are 10 possible combinations when picking two marbles from the bag.

Next, let's calculate the number of favorable outcomes, which is the number of ways to pick two red marbles from the bag. We have 3 red marbles, so we need to calculate the combinations of picking 2 out of 3:

3C2 = (3! / ((3 - 2)! * 2!))
= (3! / (1! * 2!))
= (3 * 2) / (2 * 1)
= 3

Hence, there are 3 favorable outcomes of picking two red marbles.

Finally, to find the probability of picking two red marbles, we divide the number of favorable outcomes by the number of possible outcomes:

Probability = favorable outcomes / possible outcomes
= 3 / 10

Therefore, the probability of picking two red marbles from the bag is 3/10 or 0.3, which can also be expressed as a percentage of 30%.