There are two identical boxes of balls. In the first box 2 blue and 5 orange balls, and the second 3 blue and 6 orange balls. Chosen at random from the box and pull out a 1 ball. What is the probability that the ball taken is orange
2 cases:
box 1, then orange
box 2, then orange
prob = (1/2)(5/7) + (1/2)(6/9)
= 5/14 + 6/18 = 29/42
To find the probability of pulling out an orange ball, we need to determine the total number of balls in both boxes and the number of orange balls.
Let's start with the first box. There are 2 blue and 5 orange balls, so the total number of balls in the first box is 2 + 5 = 7.
Moving on to the second box, there are 3 blue and 6 orange balls, meaning the total number of balls in the second box is 3 + 6 = 9.
Therefore, the total number of balls in both boxes combined is 7 + 9 = 16.
Now let's calculate the probability of selecting an orange ball. We know that there are a total of 16 balls, and the number of orange balls is 5 from the first box and 6 from the second box, making a total of 5 + 6 = 11 orange balls.
The probability of selecting an orange ball is calculated as:
(Number of orange balls) / (Total number of balls)
In this case, it is 11 / 16 ≈ 0.6875, or approximately 68.75%.
Therefore, the probability of pulling out an orange ball is approximately 68.75%.