# 1. You have a bag with some black balls and some white balls. You put your hand intothe bag and pull out a pair of balls.(a) If both balls are black, you throw away one and return one to the bag.(b) If both balls are white, you throw them both away.(c) If the balls are of di?erent colours, you throw away the black ball and return thewhite ball to the bag.You can keep doing this so long as there are at least two balls left in the bag. Theprocess stops when the bag is empty or has only a single ball left. Let N denote the number of times you pulledout pairs of balls. We are interested in answering the following questions.• What are the minimum and maximum values for N for which you end with asingle ball in the bag?• Is the last ball remaining in the bag always white, always black or of either colour?1In the example worked out above, if we end up with a single ball in the bag, it mustbe black. Also, the minimum and maximum values of N are both 2. Note that we arenot interested in the value of N in situations where the bag becomes empty.Compute the minimum and maximum values of N as well as the possibilities for thecolour of the last ball for each of the following initial contents of the bag.(a) 17 black balls, 23 white balls (b) 42 black balls, 32 white balls(c) 111 black balls, 99 white balls PLS anwer fast i need the solution urgently!

1. You have a bag with some black balls and some white balls. You put your hand intothe bag and pull out a pair of balls.(a) If both balls are black, you throw away one and return one to the bag.(b) If both balls are white, you throw them both away.(c) If the balls are of di?erent colours, you throw away the black ball and return thewhite ball to the bag.You can keep doing this so long as there are at least two balls left in the bag. Theprocess stops when the bag is empty or has only a single ball left. Let N denote the number of times you pulledout pairs of balls. We are interested in answering the following questions.• What are the minimum and maximum values for N for which you end with asingle ball in the bag?• Is the last ball remaining in the bag always white, always black or of either colour?1In the example worked out above, if we end up with a single ball in the bag, it mustbe black. Also, the minimum and maximum values of N are both 2. Note that we arenot interested in the value of N in situations where the bag becomes empty.Compute the minimum and maximum values of N as well as the possibilities for thecolour of the last ball for each of the following initial contents of the bag.(a) 17 black balls, 23 white balls (b) 42 black balls, 32 white balls(c) 111 black balls, 99 white balls

PLS anwer fast i need the solution urgently!