Hello, cnmath16!

Three people: John, Joan, and Kim, throw a ball to each other.

There is a probability of 1/3 that John will throw the ball to Joan.

There is a probability of 1/2 that Joan will throw the ball to Kim.

There is a probability of 1/4 that Kim will throw the ball to John.

a) Assuming that the ball starts with Joan,

what is the probability that she will have it back after 2 throws?

Then: .

Therefore, there is a probability that Joan will have the ball after 2 throws.

Correct!

We wantb) Assuming that the ball starts with Kim,

what is the probability that Joan will have it after 3 throws?

.

If the ball starts with Kim, Joan has the ball in 3 throws with probability