Question

Below are three boxes containing black and white balls. The number of each color is noted inside the box. Draw a ball from box 1 and place it in box 2. Then draw a ball from box 2 and place it in box 3. Finally draw a ball from box 3.

Box 1: 3 white, 2 black
Box 2: 2 white 2 black
Box 3: 1 white 2 black
What is the probability that the last ball, drawn from box 3, is white?

Answer 1

The probability of drawing a white ball from box 3 is 1/10.

Step-by-step explanation:

In order to calculate the probability of drawing a white ball from box 3, we need to consider all the possible outcomes. We will use the concept of conditional probability to calculate this.

1. Calculate the probability of drawing a white ball from box 1 and placing it in box 2. There are 3 white balls out of a total of 5 balls in box 1, so the probability is 3/5.
2. Calculate the probability of drawing a white ball from box 2 and placing it in box 3. After the first draw, there are 2 white balls and 2 black balls in box 2. So the probability is 2/4.
3. Finally, calculate the probability of drawing a white ball from box 3. There is 1 white ball and 2 black balls in box 3. So the probability is 1/3.

To find the probability of the last ball being white, we multiply the probabilities from each step: (3/5) * (2/4) * (1/3) = 1/10. Therefore, the probability that the last ball, drawn from box 3, is white is 1/10.