From a set of thirteen marbles, eight black and five green, we choose one at random. a. What are the odds in favor of choosing a black marble? b. What are the odds against choosing a black marble? a. The odds in favor of choosing a black marble are (Simplify your answers.)

To find the odds in favor of choosing a black marble, compare the number of favorable outcomes (black marbles) to the number of unfavorable outcomes (green marbles). There are 8 black marbles and 5 green marbles, so the odds in favor are 8:5. Now, for the odds against choosing a black marble, you simply reverse that ratio. Since there are 5 green marbles and 8 black marbles, the odds against choosing a black marble are 5:8. So, to summarize: a. The odds in favor of choosing a black marble are 8:5. b. The odds against choosing a black marble are 5:8. Did you know the concept of odds dates back centuries with roots in gambling? Ancient cultures would often use odds to determine payouts for bets! It's fascinating to see how this simple yet powerful concept continues to apply in diverse fields from statistics to finance! For those interested in mathematics or probability theory, diving into the world of combinatorics could be quite intriguing. Books like "Introduction to Probability" by Dimitri P. Bertsekas and John N. Tsitsiklis offer engaging insights into how these concepts apply to real-world situations. Grab your favorite snacks and get ready to crunch some numbers!