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

a) 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:

To find the probability that the last ball drawn from Box 3 is white, we need to consider the probabilities at each step.

Step 1: The probability of drawing a white ball from Box 1 is 3/5, since there are 3 white balls and 5 total balls.

Step 2: After transferring a ball from Box 1 to Box 2, the probabilities are as follows:

• Probability of drawing a white ball from Box 2 is 3/6, since there are 3 white balls and 6 total balls.
• Probability of drawing a black ball from Box 2 is 3/6, since there are 3 black balls and 6 total balls.

Step 3: Finally, the probability of drawing a white ball from Box 3 is 1/3, since there is 1 white ball and 3 total balls.

To find the overall probability of drawing a white ball from Box 3, we multiply the probabilities at each step: (3/5) * (3/6) * (1/3) = 1/10.