Answer plzz, probability

You have a blue bag and a red bag. The blue bag contains m blue marbles and no red marbles. The red bag contains m red marbles and no blue marbles. You decide to randomly remove marbles from these two bags. You toss a biased coin, with probability p for heads, to decide the bag from which a marble should be removed. If the coin lands on heads, you remove a single marble from the red bag. Conversely, if the coin lands on tails, you remove a single marble from the blue bag. You keep tossing the coin and keep removing marbles. At a certain point, you reach to remove a marble from one of the bags and discover that the bag is empty. Calculate the probability to have 1: remaining marbles in the other bag, where O s k g: m