A number cube is rolled and a marble is selected from a bag. There are 2 reds, 2 yellows, 2 greens, 1 blue, and 1 purple marble in the bag. Find the probability of the following: roll a 1 and pick a red marble.

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

1/6 * 2/8 = ?

To find the probability of rolling a 1 and picking a red marble, we need to determine the number of favorable outcomes (the desired outcome) and the number of possible outcomes (all the possible outcomes).

Step 1: Find the number of favorable outcomes.
Since the number cube has six faces with numbers 1 to 6, and we want to roll a 1, there is only 1 favorable outcome for the roll.

Then, for the marble selection, we want to pick a red marble, and there are 2 red marbles in the bag. Therefore, there are 2 favorable outcomes for picking a red marble.

Step 2: Find the number of possible outcomes.
Since the number cube has six faces, there are 6 possible outcomes for the roll.

For the marble selection, there are a total of 2 red marbles, 2 yellow marbles, 2 green marbles, 1 blue marble, and 1 purple marble. So, there are 2 + 2 + 2 + 1 + 1 = 8 possible outcomes for picking a marble.

Step 3: Calculate the probability.
The probability is found by dividing the number of favorable outcomes by the number of possible outcomes.

Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= (1 favorable outcome for rolling a 1) x (2 favorable outcomes for picking a red marble) / (6 possible outcomes for the roll) x (8 possible outcomes for picking a marble)

Simplifying, we have:
Probability = (1 x 2) / (6 x 8)
= 2 / 48
= 1 / 24

So, the probability of rolling a 1 and picking a red marble is 1/24 or approximately 0.0417.