I'm a probability newbie. Can anyone help me with the following problem?

A player begins with £1 and each round they can wager £1 on the outcome of a game.

The player wins the game with probability p (0.48), in which case they get £1 in winnings and with probability 1-p (0.52) the operator wins and the player loses their wager. The players play 5 repetitions.

To illustrate, on the first repetition the player either wins (with probability 0.48) and now has £2 or immediately runs out of money (with probability 0.52).

The second repetition only happens if the customer wins the first repetition. Therefore, after the second repetition the customer either wins (again with probability 0.48) and now has £3 or loses and returns to £1.

This pattern continues until the customer either runs out of money or has played five repetitions. (see the probability tree attached).

The probability that the player goes bankrupt after 1 repetition is 0.52. 1. What is the probability that the player goes bankrupt after 3 repetition? and what is the probability after 5 repetitions? Similarly, what is the probability that the players wins £2 after 5 repetitions?

How do you calculate the expected payout after 5 repetitions?

Is there a specific formula to calculate these results?

Thank you,

Fede