I have two boxes with balls; box #1 and box #2. Box #1 has 3 red balls and 2 blue balls.Box #2 has 7 red balls and 3 blue balls. what is the probability that if a red ball is picked, it is from box #1
P(Box1/Red Ball) = P(Box1+red Ball)/P(R) = (1/2 . 3/5)/ (1/2 . 3/5 + 1/2 . 7/10 ) = 6/13
To find the probability of picking a red ball from box #1, we need to calculate the ratio of the number of red balls in box #1 to the total number of balls in both boxes.
In box #1, there are 3 red balls. In box #2, there are 7 red balls. So the total number of red balls in both boxes is 3 + 7 = 10.
The total number of balls in both boxes can be calculated by adding the number of balls in each box. In box #1, there are 3 red balls + 2 blue balls = 5 balls. In box #2, there are 7 red balls + 3 blue balls = 10 balls. Therefore, the total number of balls in both boxes is 5 + 10 = 15.
Now, we can find the probability by dividing the number of desired outcomes (picking a red ball from box #1) by the total number of possible outcomes (picking any ball from both boxes).
Probability = (Number of desired outcomes) / (Total number of possible outcomes)
In this case, the number of desired outcomes is 3 (the number of red balls in box #1), and the total number of possible outcomes is 15 (the total number of balls in both boxes).
Probability = 3 / 15 = 1 / 5 = 0.2 = 20%
So, the probability of picking a red ball from box #1 is 20%.