A bag contains 4 white and 5 black balls . Another bag contains 5 white and 7 black balls . A ball is transferred from the first bag to the second and then a ball is drawn from the second bag . Find the probability that the ball drawn is white.
To find the probability that the ball drawn is white, we need to calculate the total number of possible outcomes and the number of favorable outcomes.
Let's start with the first bag:
- Initially, there are 4 white and 5 black balls, making a total of 9 balls.
Next, we transfer one ball from the first bag to the second bag. The probabilities of transferring a white or black ball are both 1.
Now, let's consider the second bag:
- After the transfer, there are 5 white and 7 black balls, making a total of 12 balls.
The probability of drawing a white ball from the second bag depends on the number of white and black balls in that bag. In this case, we have 5 white balls and 12 total balls in the second bag.
Now, we can calculate the probability as follows:
P(drawing a white ball) = Number of favorable outcomes / Total number of possible outcomes
The number of favorable outcomes is the number of white balls in the second bag, which is 5.
The total number of possible outcomes is the total number of balls in the second bag, which is 12.
Therefore, the probability of drawing a white ball from the second bag is:
P(drawing a white ball) = 5 white balls / 12 total balls
Simplifying this fraction gives:
P(drawing a white ball) = 5/12 ≈ 0.4167
So, the probability of drawing a white ball is approximately 0.4167 or 41.67%.
P(white transferred,white drawn) = 4/9 * 6/13
P(black transferred, white drawn) = 5/9 * 5/13
so, P(white drawn) = (4*6 + 5*5)/(9*13) = 49/117