WILL WARD

Note: This puzzle dates back to the 1950s, so old-fashioned assumptions were made. This is stated in the textbook as well. (a) A couple has two children. The older child is a girl. What is the probability that both children are girls? Not knowing anything else, we there are four ways in which the couple could have had two children (Here, we use the convention that the letter on the left represents the firstborn child): BB BG GB GG G - Girl, B - Boy Considering the above four scenarios, only two of them allow for the older child to be a girl: GB GG It's easy to see that the probability that both of the couple's children are girls is 1/2. (b) A couple has two children. At least one of them is…

Warning: Spoilers Follow 1. How many ways are there to permute the letters in the word MISSISSIPPI? If each letter were to have its own unique ID and it were the case that only the IDs mattered, there would be 11! permutations of the word MISSISSIPPI. However, were not permuting unique IDs, but letters, some of which get used several times, which means that 11! permutations would include overcounting. M (1 time) I (4 times) S (4 times) P (2 times) There are 4! ways in which the letters 'I' can be interchanged with each other, 4! ways in which the letters 'S' can be interchanged, and 2! ways in which the letters 'P' can be interchanged with each other. To adjust for overcounting, we divide…

Warning: Spoilers Follow A homework problem from Harvard's Stat 110 course has two chess players ready to play 7 games. The possible outcomes for each game are Win (1 point), Draw (0.5 points), and Loss (0 points). If all seven games were to be played regardless of the outcomes of the individual games, it's possible that one player could have 7 points and the other 0 points. We'll call the two players A and B. (a) How many possible outcomes for the individual games are there, such that player A has a final result of 3 wins, 2 draws, and 2 losses? First, we consider the ways in which A can get 4 wins in 7 games, . Next, we consider the ways in which A can get 2 draws in the remaining 3 games…