Question

Bob and Alice each have a bag that contains one ball of each of the colors blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and puts it into Alice's bag. What is the probability that after this process the contents of the two bags are the same

Answer 1

1/3

Explanation:

Alice can select any ball from her bag and it goes into Bob's bag. Then bob has 6 balls including two of one color.

Suppose they are {A,B,B,C,D,E}

Now Bob must draw one of the two balls of the same color (B) in order to have the same content of the two bags.

P(bags same content)= 2/6= 1/3

The probability that the bags content are the same= 1/3