Box A contains 5 red and 4 blue balls, Box Bcontains 2 red and 5 blue balls. A ball is drawnat random from each box. Find the probabilitythat one is red and the other is blue.

To find the probability that one ball is red and the other is blue, we need to consider the possible outcomes when drawing a ball from each box.

Let's start by calculating the total number of possible outcomes. In Box A, there are 5 red balls and 4 blue balls, so there are a total of 9 balls. In Box B, there are 2 red balls and 5 blue balls, so there are a total of 7 balls.

The total number of possible outcomes is the product of the number of balls in each box: 9 * 7 = 63.

Now, let's calculate the number of favorable outcomes, which is the number of outcomes where one ball is red and the other is blue.

From Box A, there are 5 red balls and 4 blue balls. If we draw a red ball from Box A, there are 2 red balls and 5 blue balls left in Box B. So, the number of favorable outcomes when drawing a red ball from Box A is 5 * 5 = 25.

Similarly, if we draw a blue ball from Box A, there are 4 red balls and 5 blue balls left in Box B. So, the number of favorable outcomes when drawing a blue ball from Box A is 4 * 5 = 20.

The total number of favorable outcomes is the sum of the favorable outcomes for each case: 25 + 20 = 45.

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: 45 / 63 = 0.7143 (rounded to four decimal places).

Therefore, the probability that one ball is red and the other is blue is approximately 0.7143.