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:
6 white
4 black

Box 2:
4 white
3 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 that the last ball, drawn from box 3, is white 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 of drawing a white ball at each step.

• Step 1: Drawing from box 1 - The probability of drawing a white ball from box 1 is 6/10.
• Step 2: Placing the ball in box 2 - The probability of drawing a white ball from box 2 depends on the color of the ball drawn from box 1. If a white ball was drawn from box 1, then the probability of drawing a white ball from box 2 is 4/8. If a black ball was drawn from box 1, then the probability of drawing a white ball from box 2 is 3/8.
• Step 3: Drawing from box 3 - The probability of drawing a white ball from box 3 depends on the color of the ball drawn from box 2. If a white ball was drawn from box 2, then the probability of drawing a white ball from box 3 is 1/3. If a black ball was drawn from box 2, then the probability of drawing a white ball from box 3 is 0/3.

To find the overall probability, we multiply the probabilities at each step: (6/10) * ((4/8) * (1/3)) + (4/10) * ((3/8) * (0/3)) = 6/60 = 1/10.