A jar contains 5 blue marble, 8 red marbles, 4 white marbles,and purple marbles. Suppose you pick a marble at random without looking. Find the probability of each event. Choosing a blue marble, putting it back, then choosing a purple? (Simplest form)

Are you given purple marbles, too?

missing information:

number of purple marbles

To find the probability of each event, we need to determine the total number of marbles in the jar and the number of marbles that satisfy each event. Let's calculate it step by step.

Step 1: Find the total number of marbles.
Total number of marbles = 5 (blue marbles) + 8 (red marbles) + 4 (white marbles) + 3 (purple marbles) = 20 marbles.

Step 2: Find the probability of choosing a blue marble.
Number of blue marbles = 5.
Probability of choosing a blue marble = Number of blue marbles / Total number of marbles = 5 / 20 = 1/4.

Step 3: Find the probability of choosing a purple marble after choosing a blue marble and putting it back.
Number of purple marbles = 3.
Probability of choosing a purple marble = Number of purple marbles / Total number of marbles = 3 / 20.

However, since we are putting the blue marble back before choosing the purple marble, these two events are independent, so we multiply the probabilities.
Probability of choosing a purple marble after choosing a blue marble = Probability of choosing a blue marble * Probability of choosing a purple marble = (1/4) * (3/20) = 3/80.

Therefore, the probability of choosing a blue marble, putting it back, and then choosing a purple marble is 3/80 in simplest form.

3 purple marbles. sorry