A bag contains 5 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green.

Sure, let's solve this step by step:

Step 1: Identify the total number of balls in each bag. Bag 1 has 5 red and 3 green balls, so a total of 8 balls. Bag 2 has 4 red and 6 green balls, so a total of 10 balls.

Step 2: Calculate the probability of drawing one red ball from Bag 1 and one green ball from Bag 2. The probability of drawing one red ball from Bag 1 is 5/8. The probability of drawing one green ball from Bag 2 is 6/10 or 3/5.

So, the combined probability of these two independent events is (5/8) * (3/5) = 15/40 = 0.375.

Step 3: Calculate the probability of drawing one green ball from Bag 1 and one red ball from Bag 2. The probability of drawing one green ball from Bag 1 is 3/8. The probability of drawing one red ball from Bag 2 is 4/10 or 2/5.

So, the combined probability of these two independent events is (3/8) * (2/5) = 6/40 = 0.15.

Step 4: Since we want the probability that one ball is red and one is green, we add the probabilities from Step 2 and Step 3. So, the total probability is 0.375 + 0.15 = 0.525.