In a bag, there are 8 red, 10 blue and 12 green balls. A ball is picked randomly from the bag and 5 blue balls are added to the bag. Now, one ball is picked randomly from the bag. What is the probability that the first ball picked is red and the second ball picked is blue?

To solve this problem, we need to calculate the probability of both events happening, which means we need to multiply the probability of the first event by the probability of the second event.

Step 1: Calculate the total number of balls in the bag initially. This is 8 red + 10 blue + 12 green = 30 balls.

Step 2: Calculate the probability of picking a red ball first. This is the number of red balls divided by the total number of balls, or 8/30 = 0.267.

Step 3: After picking one red ball, 5 blue balls are added to the bag. So, the total number of balls in the bag is now 30 - 1 (the red ball that was picked) + 5 (the blue balls that were added) = 34 balls.

Step 4: Calculate the probability of picking a blue ball second. This is the number of blue balls divided by the total number of balls, or 15/34 = 0.441.

Step 5: Multiply the two probabilities together to get the probability of both events happening. This is 0.267 * 0.441 = 0.118.

So, the probability that the first ball picked is red and the second ball picked is blue is approximately 0.118, or 11.8%.