Question

A bag has 5 red marbles, 6 blue marbles and 4 black marbles. What is the probability of picking a red
marble, replacing it, and then picking a blue marble?

Answer 1

1st marble:
The probability of drawing a red is 5/15 = 1/5 since there are 5 red ones and 15 in total

2nd marble: since you put back the red one, you still have the same amount of marbles as in the 1st draw. So the probability of picking blue is 6/15 = 2/5

Now the total probability can be worded as: P(draw red 1st AND draw blue 2nd). Because of the "AND" you should use the product rule, and not the addition rule.

P(draw red 1st AND draw blue 2nd) = P(draw red 1st) * P(draw blue 2nd) = 1/5 * 2/5